Wayground
Interior and exterior angles in polygons - Printable Math Worksheets class 12 - Wayground

Interior and exterior angles in polygons

Bobbi Garrett

Created by Bobbi Garrett

17 questions

12th Grade

Math

Updated Aug 2026

Interior and exterior angles in polygons is a Grade 12 mathematics worksheet that builds fluency with calculating angle measures and determining polygon properties. Students find the sum of interior angles, calculate one interior angle in a regular polygon, determine one exterior angle, and use a given angle sum or measure to find the number of sides. The problems include polygons such as nonagons, 15-gons, 20-gons, and 27-gons. This free printable worksheet includes an answer key and 17 questions in varied formats: 12 fill-in-the-blank items, 4 multiple-choice questions, and 1 matching activity. The matching item reinforces the relationships among interior-angle sums, exterior-angle sums, individual regular-polygon angles, and the number of sides, while the selected-response questions ask students to identify values or solve for a missing variable. It is suited to Grade 12 practice, review, or assessment after instruction on polygon angle relationships.

Worksheet settings

Font size

S
M
L
XL
WaygroundWorksheets

Interior and exterior angles in polygons

Total questions: 17

Name
Class
Date
1.

For a regular NONAGON, find the measure of one interior angle. (a)   °\degree  

2.

For a regular 15-gon, find the measure of one interior angle. (a)   °\degree  

3.

If the sum of interior angles of a polygon is  900°900\degree  , how many sides does the polygon have?



(a)  

4.

If the sum of the interior angles of a polygon is 2880°2880\degree , how many sides does the polygon have? 

(a)  

5.
Select the correct values for a and m.

Select the correct values for a and m.

a)

a=50, m=89

b)

a=50, m=116

c)

a=105, m=89

d)

a=105, m=116

6.

What is the value of each exterior angle of a regular 20-gon? (a)   °\degree   

7.

The measure of an exterior angle of a regular polygon is 45°45\degree  .

Find the number of sides of the polygon. 



(a)  

8.

Practice: The measure of an interior angle of a regular polygon is  144°144\degree  . How many sides does the polygon have?



(a)  

9.

Practice:  If the measure of one interior angle of a regular polygon is 160°160\degree  , find the number of sides. 

(a)  

10.

Match the following.

sum of the interior angle measure

(n−2)180°\left(n-2\right)180\degree

sum of the exterior angle measure

360°360\degree

one interior angle measure of a regular polygon

(n−2)180°n\frac{\left(n-2\right)180\degree}{n}

one exterior angle measure of a regular polygon

360°n\frac{360\degree}{n}

the number of sides of a regular polygon

n

11.

What is the sum of the measures of the interior angles of a 27-gon in degrees?

(a)  

12.

What is the measure of EACH interior angle of a regular 20-gon in degrees?

(a)  

13.

The sum of the interior angles of a polygon is 1620°1620\degree . How many sides does the polygon have?

a)

7

b)

9

c)

11

d)

13

14.

What is the sum of the measures of the exterior angles of a nonagon in degrees?

(a)  

15.
Find the value of x.

Find the value of x.

a)

8

b)

9

c)

10

d)

11

16.
The polygon is regular. Find the value of x.

The polygon is regular. Find the value of x.

a)

12

b)

13

c)

14

d)

15

17.
Find the value of x.

Find the value of x.

(a)  

WaygroundAnswer Key

Interior and exterior angles in polygons

Total questions: 17

1.
140, 140 degrees
2.
156, 156 degrees
3.
7, 7 sides
4.
18, 18 sides
5.
d)

a=105, m=116

6.
18, 18 degrees
7.
8, 8 sides
8.
10, 10 sides
9.
18, 18 sides
10.

sum of the interior angle measure

 - 

(n−2)180°\left(n-2\right)180\degree

, 

sum of the exterior angle measure

 - 

360°360\degree

, 

one interior angle measure of a regular polygon

 - 

(n−2)180°n\frac{\left(n-2\right)180\degree}{n}

, 

one exterior angle measure of a regular polygon

 - 

360°n\frac{360\degree}{n}

, 

the number of sides of a regular polygon

 - 

n

11.
4500
12.
162
13.
c)

11

14.
360
15.
b)

9

16.
c)

14

17.
12

Browse by subjects

Browse by grades

Browse by format

FAQs

What does the Interior and exterior angles in polygons worksheet cover?

This Grade 12 worksheet practices calculating interior-angle sums, individual interior angles, exterior angles, and the number of sides in regular polygons. Its 12 fill-in-the-blank questions require students to compute or reverse-engineer these values, while the multiple-choice and matching items reinforce angle relationships and selecting related measures.

How can I use this worksheet to teach interior and exterior angles in polygons?

Introduce the worksheet by reviewing how the number of sides determines a polygon’s interior-angle sum, then connect that sum to each interior angle in a regular polygon and to the 360-degree exterior-angle total. Have students explain the relationship before completing the fill-in-the-blank items, and use the matching activity to consolidate the meanings of the five key quantities. Finish by discussing how a known angle measure can be used to work backward to the number of sides.

What mistakes should I watch for when students complete this polygon angles worksheet?

Watch for students confusing the sum of all interior angles with one interior angle, especially in items about regular 15-gons, 20-gons, and 27-gons. Students may also use the interior-angle relationship when an exterior angle is given, forget that the exterior-angle sum is 360 degrees, or report an angle measure when the question asks for the number of sides. In the matching and multiple-choice items, check that they distinguish a total angle sum from the measure of one angle.

How do I assign and grade this interior and exterior angles worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for checking the fill-in-the-blank, multiple-choice, and matching responses. For printable submissions, you can scan student work with the Wayground for Teachers app to help grade the completed polygon-angle practice.

How can I differentiate this polygon angles worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing or choose a larger font size to make the equations, angle terms, and matching choices easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language while keeping the fill-in-the-blank, multiple-choice, and matching formats intact.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

© 2026 Wayground Inc.

Accessibility and Inclusion