# Find the number of sides when given the sum of interior angles

# Find the number of sides when given the sum of interior angles

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## Lesson details

### Key learning points

- In this lesson, we will find the number of sides of a polygon when given only the sum of interior angles.

### Licence

This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.

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### 4 Questions

Q1.

What is the sum of interior angles of a 20-sided shape?

1800º

2880º

3600º

Q2.

What is the sum of interior angles of a 9-sided shape?

1620º

1980º

900º

Q3.

What is the missing angle, labelled x?

114º

33º

Q4.

What is the size of each interior angle in a regular octagon?

225º

45º

90º

### 4 Questions

Q1.

The sum of interior angles of a polygon is 720º. How many sides does the polygon have?

5

7

8

Q2.

The sum of interior angles of a polygon is 2880º. How many sides does the polygon have?

15

16

17

Q3.

The sum of interior angles of a regular polygon is 3960º. What is the size of each interior angle of the regular polygon?

150º

170º

175º

Q4.

The sum of interior angles of a regular polygon is 5040º. What is the size of each exterior angle of the regular polygon?

100.8º

168º

79.2º