# 6.2.3 Polygon Angle Sums

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When finding the angles of a polygon, we usually divide the polygon into triangles. There is a basic formula for getting the angles that was covered in class today. Take up the quiz below to help you practice on getting the angles of a polygon until it sticks. Best of luck!

• 1.

### What is the interior angle sum of a decagon?

• A.

1800 degrees

• B.

1440 degrees

• C.

1080 degrees

• D.

720 degrees

• E.

360 degrees

B. 1440 degrees
Explanation
A decagon is a polygon with ten sides. To find the interior angle sum of a decagon, we can use the formula (n-2) * 180, where n is the number of sides. Plugging in 10 for n, we get (10-2) * 180 = 8 * 180 = 1440 degrees. Therefore, the correct answer is 1440 degrees.

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• 2.

### What is the interior angle sum of a pentagon?

• A.

360 degrees

• B.

540 degrees

• C.

720 degrees

• D.

900 degrees

• E.

1080 degrees

B. 540 degrees
Explanation
The interior angle sum of a polygon is given by the formula (n-2) * 180, where n is the number of sides of the polygon. In the case of a pentagon (a polygon with 5 sides), the formula becomes (5-2) * 180 = 3 * 180 = 540 degrees. Therefore, the correct answer is 540 degrees.

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• 3.

### What is the interior angle sum of an octagon?

• A.

360 degrees

• B.

540 degrees

• C.

720 degrees

• D.

900 degrees

• E.

1080 degrees

E. 1080 degrees
Explanation
An octagon has 8 sides. To find the interior angle sum of any polygon, we use the formula (n-2) * 180 degrees, where n is the number of sides. Substituting n=8, we get (8-2) * 180 = 6 * 180 = 1080 degrees. Therefore, the correct answer is 1080 degrees.

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• 4.

### What is the exterior angle sum of a pentagon?

• A.

360 degrees

• B.

540 degrees

• C.

720 degrees

• D.

900 degrees

• E.

1080 degrees

A. 360 degrees
Explanation
Exterior angle sum of any polygon = 360

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• 5.

### What is the measure in degrees of one exterior angle of a regular octagon?

• A.

20

• B.

30

• C.

36

• D.

40

• E.

45

E. 45
Explanation
The measure in degrees of one exterior angle of a regular octagon is 45. In a regular octagon, all the exterior angles are congruent, meaning they have the same measure. Since there are 8 exterior angles in an octagon and the sum of the exterior angles of any polygon is always 360 degrees, we can divide 360 by 8 to find the measure of each exterior angle. 360/8 = 45. Therefore, each exterior angle of a regular octagon measures 45 degrees.

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• 6.

### What is the measure in degrees of one exterior angle of a regular nonegon?

• A.

20

• B.

30

• C.

40

• D.

60

• E.

90

C. 40
Explanation
The measure in degrees of one exterior angle of a regular nonagon is 40. In a regular nonagon, there are nine equal exterior angles that add up to 360 degrees. Therefore, each exterior angle is 360 degrees divided by 9, which equals 40 degrees.

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• 7.

### How many sides does a regular polygon have if each exterior angle measures 20 degrees?

• A.

18

• B.

12

• C.

10

• D.

9

• E.

8

A. 18
Explanation
A regular polygon is a polygon that has all sides of equal length and all angles of equal measure. The sum of the exterior angles of any polygon is always 360 degrees. Since each exterior angle measures 20 degrees, we can divide 360 by 20 to find the number of sides. 360/20 = 18. Therefore, a regular polygon with each exterior angle measuring 20 degrees has 18 sides.

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• 8.

### How many sides does a regular polygon have if each exterior angle measures 60 degrees?

• A.

10

• B.

9

• C.

8

• D.

7

• E.

6

E. 6
Explanation
A regular polygon is a polygon with all sides and angles equal. The sum of the exterior angles of any polygon is always 360 degrees. If each exterior angle of a regular polygon measures 60 degrees, then there must be 6 sides in the polygon. This is because 360 divided by 60 equals 6. Therefore, the correct answer is 6.

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• 9.

### What is the measure of one interior angle of a regular pentagon?

• A.

108 degrees

• B.

120 degrees

• C.

135 degrees

• D.

144 degrees

• E.

150 degrees

A. 108 degrees
Explanation
The measure of one interior angle of a regular pentagon is 108 degrees. A regular pentagon has five sides and five interior angles. To find the measure of one interior angle, we can use the formula (n-2) * 180 / n, where n is the number of sides of the polygon. Plugging in the values, we get (5-2) * 180 / 5 = 3 * 180 / 5 = 540 / 5 = 108. Therefore, the measure of one interior angle of a regular pentagon is 108 degrees.

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• 10.

### What is the measure of one interior angle of a regular decagon?

• A.

108

• B.

120 degrees

• C.

135 degrees

• D.

144 degrees

• E.

150 degrees

D. 144 degrees
Explanation
A regular decagon has 10 equal sides and 10 equal interior angles. To find the measure of one interior angle, we divide the sum of all interior angles (180 degrees) by the number of angles, which is 10. Therefore, each interior angle of a regular decagon measures 180/10 = 18 degrees.

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• Current Version
• Mar 21, 2023
Quiz Edited by
ProProfs Editorial Team
• Mar 27, 2010
Quiz Created by
Annacabral

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