Quick Answer
SAT polygon angle properties practice questions test interior-angle sums, exterior angles, regular polygons, central angles, quadrilateral properties, algebraic expressions, and side-count relationships.
What Should You Know?
- Interior-angle sum=(n-2)180°.
- Exterior-angle sum=360°.
- Regular exterior angle=360°/n.
- Regular interior angle=180°-360°/n.
- Central angle=360°/n.
- Opposite parallelogram angles are equal.
- Adjacent parallelogram angles are supplementary.
- Isosceles trapezoid base angles are equal.
In This Guide
Start With SAT Math Topic-Wise Practice
Connect polygon-angle practice with weekly score planning and targeted SAT Math correction.
Download the SAT Prep Guide E-Book
Organize polygon formulas and weekly SAT Math practice with a clear study plan.
Download SAT Prep Guide E-BookWhat Does the SAT Test in Polygon Angle Properties Questions?
Students may need to calculate an angle sum, determine a side count, use exterior or central angles, apply quadrilateral properties, or solve algebraic angle expressions.
| Skill Area | What It Tests | Questions |
|---|---|---|
| Interior sums | Totals, missing angles, side counts | Q1-Q15 |
| Regular polygons | Interior, exterior, central angles | Q16-Q30 |
| Quadrilaterals | Parallelograms, trapezoids, kites | Q31-Q45 |
| Advanced | Algebraic models and high-side-count polygons | Q46-Q70 |
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How Are Polygon Interior-Angle Sums Tested?
Use (n-2)180° to find totals, missing angles, and side counts.
POLYGON INTERIOR ANGLE BASICS
EASY
Question 1
What is the sum of the interior angles of a triangle?
Which choice is correct?
A) 0°
B) 180°
C) 360°
D) 540°
Show full solution
Correct answer: B) 180°
Use (n-2)180° with n=3: (3-2)180°=180°.
SAT trap: Use n-2, not n.
POLYGON INTERIOR ANGLE BASICS
EASY
Question 2
What is the sum of the interior angles of a quadrilateral?
Which choice is correct?
A) 180°
B) 360°
C) 540°
D) 720°
Show full solution
Correct answer: B) 360°
Use (n-2)180° with n=4: (4-2)180°=360°.
SAT trap: Use n-2, not n.
POLYGON INTERIOR ANGLE BASICS
EASY
Question 3
What is the sum of the interior angles of a pentagon?
Which choice is correct?
A) 360°
B) 540°
C) 720°
D) 900°
Show full solution
Correct answer: B) 540°
Use (n-2)180° with n=5: (5-2)180°=540°.
SAT trap: Use n-2, not n.
POLYGON INTERIOR ANGLE BASICS
EASY
Question 4
What is the sum of the interior angles of a hexagon?
Which choice is correct?
A) 540°
B) 720°
C) 900°
D) 1080°
Show full solution
Correct answer: B) 720°
Use (n-2)180° with n=6: (6-2)180°=720°.
SAT trap: Use n-2, not n.
POLYGON INTERIOR ANGLE BASICS
EASY
Question 5
What is the sum of the interior angles of a octagon?
Which choice is correct?
A) 900°
B) 1080°
C) 1260°
D) 1440°
Show full solution
Correct answer: B) 1080°
Use (n-2)180° with n=8: (8-2)180°=1080°.
SAT trap: Use n-2, not n.
POLYGON INTERIOR ANGLE BASICS
EASY
Question 6
What is the sum of the interior angles of a decagon?
Which choice is correct?
A) 1260°
B) 1440°
C) 1620°
D) 1800°
Show full solution
Correct answer: B) 1440°
Use (n-2)180° with n=10: (10-2)180°=1440°.
SAT trap: Use n-2, not n.
POLYGON INTERIOR ANGLE BASICS
MEDIUM
Question 7
A polygon has an interior-angle sum of 900°. How many sides does it have?
Which choice is correct?
A) 6
B) 7
C) 8
D) 9
Show full solution
Correct answer: B) 7
(n-2)180=900, so n-2=5 and n=7.
SAT trap: Divide by 180 before adding 2.
POLYGON INTERIOR ANGLE BASICS
MEDIUM
Question 8
A polygon has an interior-angle sum of 1260°. How many sides does it have?
Which choice is correct?
A) 8
B) 9
C) 10
D) 11
Show full solution
Correct answer: B) 9
(n-2)180=1260, so n-2=7 and n=9.
SAT trap: Divide by 180 before adding 2.
POLYGON INTERIOR ANGLE BASICS
MEDIUM
Question 9
A polygon has an interior-angle sum of 1800°. How many sides does it have?
Which choice is correct?
A) 11
B) 12
C) 13
D) 14
Show full solution
Correct answer: B) 12
(n-2)180=1800, so n-2=10 and n=12.
SAT trap: Divide by 180 before adding 2.
POLYGON INTERIOR ANGLE BASICS
MEDIUM
Question 10
A polygon has an interior-angle sum of 2340°. How many sides does it have?
Which choice is correct?
A) 14
B) 15
C) 16
D) 17
Show full solution
Correct answer: B) 15
(n-2)180=2340, so n-2=13 and n=15.
SAT trap: Divide by 180 before adding 2.
POLYGON INTERIOR ANGLE BASICS
MEDIUM
Question 11
How many triangles can be formed by drawing diagonals from one vertex of a 9-sided polygon?
Which choice is correct?
A) 6
B) 7
C) 8
D) 9
Show full solution
Correct answer: B) 7
The number of triangles is n-2=7.
SAT trap: Use n-2.
POLYGON INTERIOR ANGLE BASICS
MEDIUM
Question 12
How many triangles can be formed by drawing diagonals from one vertex of a 14-sided polygon?
Which choice is correct?
A) 11
B) 12
C) 13
D) 14
Show full solution
Correct answer: B) 12
The number of triangles is n-2=12.
SAT trap: Use n-2.
POLYGON INTERIOR ANGLE BASICS
MEDIUM
Question 13
A pentagon has four angles of 100°, 110°, 120°, and 90°. What is the fifth angle?
Which choice is correct?
A) 100°
B) 110°
C) 120°
D) 130°
Show full solution
Correct answer: C) 120°
The pentagon sum is 540°. The known angles total 420°, leaving 120°.
SAT trap: Find the total before subtracting.
POLYGON INTERIOR ANGLE BASICS
MEDIUM
Question 14
A hexagon has five interior angles of 120° each. What is the sixth angle?
Which choice is correct?
A) 90°
B) 100°
C) 110°
D) 120°
Show full solution
Correct answer: D) 120°
The hexagon sum is 720°. Five angles total 600°, leaving 120°.
SAT trap: Use the 720° total.
POLYGON INTERIOR ANGLE BASICS
MEDIUM
Question 15
Why does the interior-angle sum increase by 180° when one side is added?
Which choice is correct?
A) One exterior angle is added
B) One more triangle is formed
C) The polygon becomes regular
D) The perimeter doubles
Show full solution
Correct answer: B) One more triangle is formed
Increasing n by 1 creates one additional triangle in the triangulation.
SAT trap: Connect the formula to triangles.
Build Stronger SAT Geometry Skills
Connect polygon formulas with algebra and real SAT Math timing.
How Are Regular Polygons and Exterior Angles Tested?
Use equal interior, exterior, and central angles.
REGULAR POLYGONS AND EXTERIOR ANGLES
MEDIUM
Question 16
What is each exterior angle of a regular 3-gon?
Which choice is correct?
A) 60°
B) 120°
C) 60°
D) 240°
Show full solution
Correct answer: B) 120°
Each exterior angle is 360°/3=120°.
SAT trap: Divide 360° by the number of sides.
REGULAR POLYGONS AND EXTERIOR ANGLES
MEDIUM
Question 17
What is each exterior angle of a regular 4-gon?
Which choice is correct?
A) 45°
B) 90°
C) 90°
D) 270°
Show full solution
Correct answer: B) 90°
Each exterior angle is 360°/4=90°.
SAT trap: Divide 360° by the number of sides.
REGULAR POLYGONS AND EXTERIOR ANGLES
MEDIUM
Question 18
What is each exterior angle of a regular 5-gon?
Which choice is correct?
A) 36°
B) 72°
C) 108°
D) 288°
Show full solution
Correct answer: B) 72°
Each exterior angle is 360°/5=72°.
SAT trap: Divide 360° by the number of sides.
REGULAR POLYGONS AND EXTERIOR ANGLES
MEDIUM
Question 19
What is each exterior angle of a regular 6-gon?
Which choice is correct?
A) 30°
B) 60°
C) 120°
D) 300°
Show full solution
Correct answer: B) 60°
Each exterior angle is 360°/6=60°.
SAT trap: Divide 360° by the number of sides.
REGULAR POLYGONS AND EXTERIOR ANGLES
MEDIUM
Question 20
What is each exterior angle of a regular 8-gon?
Which choice is correct?
A) 22°
B) 45°
C) 135°
D) 315°
Show full solution
Correct answer: B) 45°
Each exterior angle is 360°/8=45°.
SAT trap: Divide 360° by the number of sides.
REGULAR POLYGONS AND EXTERIOR ANGLES
MEDIUM
Question 21
What is each exterior angle of a regular 10-gon?
Which choice is correct?
A) 18°
B) 36°
C) 144°
D) 324°
Show full solution
Correct answer: B) 36°
Each exterior angle is 360°/10=36°.
SAT trap: Divide 360° by the number of sides.
REGULAR POLYGONS AND EXTERIOR ANGLES
MEDIUM
Question 22
What is each interior angle of a regular 5-gon?
Which choice is correct?
A) 90°
B) 108°
C) 117°
D) 126°
Show full solution
Correct answer: B) 108°
Each exterior angle is 360°/5; subtract it from 180° to get 108°.
SAT trap: Interior and exterior angles are supplementary.
REGULAR POLYGONS AND EXTERIOR ANGLES
MEDIUM
Question 23
What is each interior angle of a regular 6-gon?
Which choice is correct?
A) 102°
B) 120°
C) 129°
D) 138°
Show full solution
Correct answer: B) 120°
Each exterior angle is 360°/6; subtract it from 180° to get 120°.
SAT trap: Interior and exterior angles are supplementary.
REGULAR POLYGONS AND EXTERIOR ANGLES
MEDIUM
Question 24
What is each interior angle of a regular 8-gon?
Which choice is correct?
A) 117°
B) 135°
C) 144°
D) 153°
Show full solution
Correct answer: B) 135°
Each exterior angle is 360°/8; subtract it from 180° to get 135°.
SAT trap: Interior and exterior angles are supplementary.
REGULAR POLYGONS AND EXTERIOR ANGLES
MEDIUM
Question 25
What is each interior angle of a regular 10-gon?
Which choice is correct?
A) 126°
B) 144°
C) 153°
D) 162°
Show full solution
Correct answer: B) 144°
Each exterior angle is 360°/10; subtract it from 180° to get 144°.
SAT trap: Interior and exterior angles are supplementary.
REGULAR POLYGONS AND EXTERIOR ANGLES
HARD
Question 26
A regular polygon has exterior angles of 30°. How many sides does it have?
Which choice is correct?
A) 10
B) 12
C) 15
D) 18
Show full solution
Correct answer: B) 12
n=360°/30°=12.
SAT trap: The side count must be a whole number.
REGULAR POLYGONS AND EXTERIOR ANGLES
HARD
Question 27
A regular polygon has exterior angles of 24°. How many sides does it have?
Which choice is correct?
A) 13
B) 15
C) 18
D) 21
Show full solution
Correct answer: B) 15
n=360°/24°=15.
SAT trap: The side count must be a whole number.
REGULAR POLYGONS AND EXTERIOR ANGLES
HARD
Question 28
A regular polygon has interior angles of 150°. How many sides does it have?
Which choice is correct?
A) 9
B) 12
C) 15
D) 18
Show full solution
Correct answer: B) 12
The exterior angle is 30°, so n=360/30=12.
SAT trap: Convert interior to exterior first.
REGULAR POLYGONS AND EXTERIOR ANGLES
HARD
Question 29
A regular polygon has interior angles of 156°. How many sides does it have?
Which choice is correct?
A) 12
B) 15
C) 18
D) 21
Show full solution
Correct answer: B) 15
The exterior angle is 24°, so n=360/24=15.
SAT trap: Convert interior to exterior first.
REGULAR POLYGONS AND EXTERIOR ANGLES
HARD
Question 30
What is each central angle of a regular nonagon?
Which choice is correct?
A) 30°
B) 40°
C) 45°
D) 50°
Show full solution
Correct answer: B) 40°
360°/9=40°.
SAT trap: Central angles split a full circle equally.
How Are Quadrilateral Angle Properties Tested?
Use parallelogram, rectangle, rhombus, kite, and trapezoid relationships.
QUADRILATERAL ANGLE PROPERTIES
HARD
Question 31
In a parallelogram, one angle is 70°. What is the opposite angle?
Which choice is correct?
A) 70°
B) 90°
C) 110°
D) 140°
Show full solution
Correct answer: A) 70°
Opposite angles are congruent.
SAT trap: Do not use supplementary for opposite angles.
QUADRILATERAL ANGLE PROPERTIES
HARD
Question 32
In a parallelogram, one angle is 70°. What is an adjacent angle?
Which choice is correct?
A) 70°
B) 90°
C) 110°
D) 140°
Show full solution
Correct answer: C) 110°
Adjacent angles are supplementary: 180-70=110°.
SAT trap: Adjacent angles sum to 180°.
QUADRILATERAL ANGLE PROPERTIES
HARD
Question 33
A rectangle has one interior angle of 90°. What are the other three angles?
Which choice is correct?
A) 60°,90°,120°
B) 90°,90°,90°
C) 45°,90°,135°
D) 80°,90°,100°
Show full solution
Correct answer: B) 90°,90°,90°
All rectangle angles are right angles.
SAT trap: A rectangle is equiangular.
QUADRILATERAL ANGLE PROPERTIES
HARD
Question 34
A rhombus has one angle of 112°. What is the opposite angle?
Which choice is correct?
A) 68°
B) 90°
C) 112°
D) 248°
Show full solution
Correct answer: C) 112°
A rhombus is a parallelogram, so opposite angles are equal.
SAT trap: Equal sides do not make all angles equal.
QUADRILATERAL ANGLE PROPERTIES
HARD
Question 35
A rhombus has one angle of 112°. What is an adjacent angle?
Which choice is correct?
A) 68°
B) 90°
C) 112°
D) 248°
Show full solution
Correct answer: A) 68°
180-112=68°.
SAT trap: Adjacent angles are supplementary.
QUADRILATERAL ANGLE PROPERTIES
HARD
Question 36
What is each exterior angle of a square?
Which choice is correct?
A) 45°
B) 60°
C) 90°
D) 120°
Show full solution
Correct answer: C) 90°
Each interior angle is 90°, so the adjacent exterior angle is 90°.
SAT trap: Interior plus exterior equals 180°.
QUADRILATERAL ANGLE PROPERTIES
HARD
Question 37
An isosceles trapezoid has one base angle of 65°. What is the other angle on the same base?
Which choice is correct?
A) 65°
B) 90°
C) 115°
D) 130°
Show full solution
Correct answer: A) 65°
Base angles are congruent.
SAT trap: Angles on the same base are equal.
QUADRILATERAL ANGLE PROPERTIES
HARD
Question 38
An isosceles trapezoid has a lower base angle of 65°. What is an upper base angle?
Which choice is correct?
A) 65°
B) 90°
C) 115°
D) 130°
Show full solution
Correct answer: C) 115°
Consecutive angles along a leg are supplementary.
SAT trap: Same-leg angles sum to 180°.
QUADRILATERAL ANGLE PROPERTIES
HARD
Question 39
In a kite, the opposite angles between unequal sides are what?
Which choice is correct?
A) Complementary
B) Congruent
C) Supplementary
D) Unrelated
Show full solution
Correct answer: B) Congruent
That pair of opposite angles is congruent.
SAT trap: Not both opposite pairs are equal.
QUADRILATERAL ANGLE PROPERTIES
HARD
Question 40
A quadrilateral has angles 80°,95°,110°, and x°. What is x?
Which choice is correct?
A) 65°
B) 70°
C) 75°
D) 85°
Show full solution
Correct answer: C) 75°
x=360-80-95-110=75°.
SAT trap: Quadrilateral angles total 360°.
QUADRILATERAL ANGLE PROPERTIES
HARD
Question 41
A parallelogram has adjacent angles (3x+10)° and (5x-6)°. What is x?
Which choice is correct?
A) 18
B) 20
C) 22
D) 24
Show full solution
Correct answer: C) 22
3x+10+5x-6=180, so 8x=176 and x=22.
SAT trap: Set adjacent angles equal to 180°.
QUADRILATERAL ANGLE PROPERTIES
HARD
Question 42
Opposite angles of a parallelogram are (4x+8)° and (6x-22)°. What is x?
Which choice is correct?
A) 10
B) 12
C) 15
D) 18
Show full solution
Correct answer: C) 15
4x+8=6x-22, so x=15.
SAT trap: Opposite angles are equal.
QUADRILATERAL ANGLE PROPERTIES
HARD
Question 43
An isosceles trapezoid has base angles (2x+5)° and (4x-35)°. What is x?
Which choice is correct?
A) 15
B) 20
C) 25
D) 30
Show full solution
Correct answer: B) 20
2x+5=4x-35, so x=20.
SAT trap: Same-base angles are equal.
QUADRILATERAL ANGLE PROPERTIES
HARD
Question 44
A rhombus has one angle twice an adjacent angle. What is the smaller angle?
Which choice is correct?
A) 45°
B) 60°
C) 90°
D) 120°
Show full solution
Correct answer: B) 60°
x+2x=180, so x=60°.
SAT trap: Adjacent angles are supplementary.
QUADRILATERAL ANGLE PROPERTIES
HARD
Question 45
Which statement is always true about a rectangle?
Which choice is correct?
A) Opposite angles are unequal
B) Every corner angle is 90°
C) Adjacent angles total 90°
D) Only two angles are right
Show full solution
Correct answer: B) Every corner angle is 90°
All rectangle angles are right angles.
SAT trap: Do not confuse diagonal angles with corner angles.
Practice More SAT Polygon and Quadrilateral Math
Build accuracy with regular polygons and quadrilateral properties.
How Are Algebraic Polygon Angles Tested?
Combine formulas with variables, ratios, and regular-polygon conditions.
ALGEBRAIC POLYGON ANGLES
HARD
Question 46
The angles of a pentagon are x°,x°,2x°,2x°,3x°. What is x?
Which choice is correct?
A) 45
B) 54
C) 60
D) 72
Show full solution
Correct answer: C) 60
9x=540, so x=60.
SAT trap: Use the pentagon total.
ALGEBRAIC POLYGON ANGLES
HARD
Question 47
A hexagon has five equal angles x° and one angle of 120°. What is x?
Which choice is correct?
A) 108
B) 120
C) 126
D) 132
Show full solution
Correct answer: B) 120
5x+120=720, so x=120.
SAT trap: Use the hexagon total.
ALGEBRAIC POLYGON ANGLES
HARD
Question 48
A regular polygon has each interior angle 140°. How many sides?
Which choice is correct?
A) 8
B) 9
C) 10
D) 12
Show full solution
Correct answer: B) 9
Exterior=40°, so n=360/40=9.
SAT trap: Convert interior to exterior.
ALGEBRAIC POLYGON ANGLES
HARD
Question 49
A regular polygon has each interior angle 165°. How many sides?
Which choice is correct?
A) 18
B) 20
C) 24
D) 30
Show full solution
Correct answer: C) 24
Exterior=15°, so n=24.
SAT trap: Subtract from 180°.
ALGEBRAIC POLYGON ANGLES
HARD
Question 50
The exterior angles of a polygon are 50°,70°,80°,60°, and x°. What is x?
Which choice is correct?
A) 80°
B) 90°
C) 100°
D) 110°
Show full solution
Correct answer: C) 100°
Exterior angles total 360°, and the known angles total 260°.
SAT trap: Use the 360° total.
ALGEBRAIC POLYGON ANGLES
HARD
Question 51
A polygon has one exterior angle of 40° and eight equal exterior angles x°. What is x?
Which choice is correct?
A) 35°
B) 40°
C) 45°
D) 50°
Show full solution
Correct answer: B) 40°
40+8x=360, so x=40°.
SAT trap: Count all exterior angles.
ALGEBRAIC POLYGON ANGLES
HARD
Question 52
A regular polygon has twice as many sides as a hexagon. What is each exterior angle?
Which choice is correct?
A) 20°
B) 30°
C) 45°
D) 60°
Show full solution
Correct answer: B) 30°
It has 12 sides, so 360/12=30°.
SAT trap: Find the side count first.
ALGEBRAIC POLYGON ANGLES
HARD
Question 53
A regular polygon exterior angle is half that of a regular pentagon. How many sides?
Which choice is correct?
A) 8
B) 10
C) 12
D) 15
Show full solution
Correct answer: B) 10
Pentagon exterior=72°. Half is 36°, so n=10.
SAT trap: Compare exterior angles.
ALGEBRAIC POLYGON ANGLES
HARD
Question 54
A polygon interior sum is 360° greater than an octagon. How many sides?
Which choice is correct?
A) 9
B) 10
C) 11
D) 12
Show full solution
Correct answer: B) 10
Octagon sum=1080°. Add 360° to get 1440°, which is a decagon.
SAT trap: Each extra side adds 180°.
ALGEBRAIC POLYGON ANGLES
HARD
Question 55
A regular polygon has central angle 24°. What is each interior angle?
Which choice is correct?
A) 144°
B) 150°
C) 156°
D) 162°
Show full solution
Correct answer: C) 156°
Central=exterior=24°, so interior=156°.
SAT trap: Central and exterior angles match.
What Do Hard Mixed Polygon Angle Questions Look Like?
Combine many-sided polygons, small exterior angles, and multi-step equations.
HARD MIXED POLYGON ANGLES
HARD
Question 56
A regular 20-gon has what interior angle?
Which choice is correct?
A) 144°
B) 150°
C) 156°
D) 162°
Show full solution
Correct answer: D) 162°
Exterior=18°, so interior=162°.
SAT trap: Use 180°-360°/n.
HARD MIXED POLYGON ANGLES
HARD
Question 57
A regular 24-gon has what exterior angle?
Which choice is correct?
A) 12°
B) 15°
C) 18°
D) 24°
Show full solution
Correct answer: B) 15°
360/24=15°.
SAT trap: Divide the full turn.
HARD MIXED POLYGON ANGLES
HARD
Question 58
A regular polygon has interior angle 168°. How many sides?
Which choice is correct?
A) 24
B) 30
C) 36
D) 40
Show full solution
Correct answer: B) 30
Exterior=12°, so n=30.
SAT trap: Small exterior angles mean many sides.
HARD MIXED POLYGON ANGLES
HARD
Question 59
An 18-sided polygon has what interior-angle sum?
Which choice is correct?
A) 2520°
B) 2700°
C) 2880°
D) 3060°
Show full solution
Correct answer: C) 2880°
(18-2)180=2880°.
SAT trap: Use n-2.
HARD MIXED POLYGON ANGLES
HARD
Question 60
A regular 15-gon has what interior angle?
Which choice is correct?
A) 144°
B) 150°
C) 156°
D) 160°
Show full solution
Correct answer: C) 156°
Exterior=24°, so interior=156°.
SAT trap: 15 exterior angles total 360°.
HARD MIXED POLYGON ANGLES
HARD
Question 61
A regular polygon has exterior angle 7.5°. How many sides?
Which choice is correct?
A) 36
B) 42
C) 48
D) 54
Show full solution
Correct answer: C) 48
360/7.5=48.
SAT trap: Decimal exterior angles are valid.
HARD MIXED POLYGON ANGLES
HARD
Question 62
A polygon interior-angle sum is 3420°. How many sides?
Which choice is correct?
A) 19
B) 20
C) 21
D) 22
Show full solution
Correct answer: C) 21
3420/180=19, then add 2.
SAT trap: Add 2 after dividing.
HARD MIXED POLYGON ANGLES
HARD
Question 63
A regular polygon interior angle is 12 times its exterior angle. How many sides?
Which choice is correct?
A) 24
B) 26
C) 28
D) 30
Show full solution
Correct answer: B) 26
12x+x=180, so x=180/13 and n=26.
SAT trap: Interior and exterior form a linear pair.
HARD MIXED POLYGON ANGLES
HARD
Question 64
A regular polygon interior angle is 8 times its exterior angle. How many sides?
Which choice is correct?
A) 16
B) 18
C) 20
D) 24
Show full solution
Correct answer: B) 18
8x+x=180, so x=20° and n=18.
SAT trap: Solve for the exterior angle first.
HARD MIXED POLYGON ANGLES
HARD
Question 65
The difference between each interior and exterior angle of a regular polygon is 120°. How many sides?
Which choice is correct?
A) 10
B) 12
C) 15
D) 18
Show full solution
Correct answer: B) 12
I+E=180 and I-E=120, so E=30° and n=12.
SAT trap: Use both equations.
What Do Student-Produced Responses Look Like?
Enter the requested angle sum, side count, or angle measure.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 66
What is the interior-angle sum of a 13-sided polygon?
Enter your answer.
Show full solution
Correct answer: 1980
(13-2)180=1980.
SAT trap: Enter only the requested numerical value.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 67
A regular polygon has exterior angles of 20°. How many sides?
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Correct answer: 18
360/20=18.
SAT trap: Enter only the requested numerical value.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 68
What is each interior angle of a regular octagon?
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Correct answer: 135
Exterior=45°, so interior=135°.
SAT trap: Enter only the requested numerical value.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 69
A quadrilateral has angles 85°,95°,110°, and x°. What is x?
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Correct answer: 70
360-85-95-110=70.
SAT trap: Enter only the requested numerical value.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 70
A regular polygon has a central angle of 15°. How many sides?
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Correct answer: 24
360/15=24.
SAT trap: Enter only the requested numerical value.
Common SAT Polygon Angle Mistakes
| Mistake | Correction |
|---|---|
| Using n×180° | Use (n-2)180° |
| Forgetting exterior total | Exterior angles total 360° |
| Setting adjacent parallelogram angles equal | They are supplementary |
| Using regular formulas on irregular polygons | Equal-angle formulas require regular polygons |
Two-Week SAT Polygon Angle Study Plan
| Days | Focus |
|---|---|
| 1-3 | Q1-Q15 |
| 4-7 | Q16-Q30 |
| 8-10 | Q31-Q45 |
| 11-14 | Q46-Q70 and review |
Frequently Asked Questions About SAT Polygon Angle Properties Practice Questions
Are polygon angle properties tested on the Digital SAT?
Yes. They may appear in Geometry and Trigonometry questions.
What is the interior-angle sum formula?
For an n-sided polygon, use (n-2)180°.
What is the exterior-angle sum?
The exterior angles of any polygon sum to 360°.
How do I find each exterior angle of a regular polygon?
Divide 360° by the number of sides.
How do I find each interior angle of a regular polygon?
Subtract the exterior angle from 180°.
What are parallelogram angle properties?
Opposite angles are equal and adjacent angles are supplementary.
What are isosceles trapezoid angle properties?
Base angles are equal and same-leg angles are supplementary.
How many questions should I practice?
Practice interior sums, exterior angles, regular polygons, quadrilaterals, and algebraic models.
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