Geometry Practice Test: Interior and Exterior Angles of Polygons
- Polygon Interior Angles
- 10 questions
- 12 minutes
The key formulas are (n − 2) · 180° for the interior angle sum and 360° for the exterior angle sum of any convex polygon. Tip: for regular polygons, the exterior angle is often the quickest way in.
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Question 1
What is the sum of the interior angles of a convex nonagon (9 sides)?
Correct answer: B
The sum is (n − 2) · 180° = 7 · 180° = 1260°. The value 1620° uses 9 · 180° and forgets to subtract 2.
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Question 2
What is the measure of each interior angle of a regular decagon (10 sides)?
Correct answer: D
Each exterior angle is 360°/10 = 36°, so each interior angle is 180° − 36° = 144°. The value 140° belongs to a regular nonagon.
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Question 3
The interior angles of a convex polygon add up to 2340°. How many sides does the polygon have?
Correct answer: C
Solve (n − 2) · 180 = 2340: n − 2 = 13, so n = 15. Answering 13 forgets to add the 2 back.
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Question 4
Each interior angle of a regular polygon measures 160°. How many sides does it have?
Correct answer: A
Each exterior angle is 180° − 160° = 20°, and 360°/20° = 18 sides. The answer 20 is the exterior angle, not the number of sides.
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Question 5
A convex pentagon has angles of 100°, 120°, 95°, 110° and x°.
What is the value of x?
Correct answer: B
A pentagon's angles add up to 3 · 180° = 540°. The four known angles total 425°, so x = 540 − 425 = 115.
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Question 6
One exterior angle is drawn at each vertex of a convex 12-sided polygon. What is the sum of these exterior angles?
Correct answer: D
For every convex polygon, taking one exterior angle at each vertex gives a total of 360°, whatever the number of sides. The value 1800° is the interior angle sum of a 12-gon.
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Question 7
Five of the interior angles of a convex hexagon measure 118° each.
What is the measure of the sixth angle?
Correct answer: C
A hexagon's angles add up to 4 · 180° = 720°. The five angles total 590°, so the sixth is 720° − 590° = 130°.
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Question 8
Which measure cannot be the measure of each interior angle of a regular polygon?
Correct answer: A
An interior angle of 130° would mean an exterior angle of 50°, and 360/50 = 7.2 is not a whole number of sides. The others give 6, 8 and 9 sides.
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Question 9
In a regular polygon, each interior angle is 4 times as large as each exterior angle. How many sides does the polygon have?
Correct answer: B
Interior + exterior = 180°, so 5e = 180° and e = 36°. Then n = 360°/36° = 10.
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Question 10
The angles of a convex quadrilateral are in the ratio 2 : 3 : 3 : 4.
What is the measure of the largest angle?
Correct answer: D
The angles add up to 360°, and 2 + 3 + 3 + 4 = 12 parts, so one part is 30°. The largest angle is 4 · 30° = 120°.
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