# Interior Angles of Regular Polygons

In this worksheet, students calculate the interior angle of regular polygons. Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Derive/Use the Sum of Angles for Deduction

Difficulty level:   ### QUESTION 1 of 10

Regular polygons have interior angles which are all equal to each other.

To work out the sum of the interior angles of a polygon, we first work out the sum of its angles by splitting it into triangles.

We then divide this sum by the number of angles.

Example

Work out the interior angle of a regular hexagon.

The hexagon can be split into triangles. There are 4 triangles inside the hexagon.

4 x 180º = 720º

The sum of the interior angles of a hexagon is 720º.

There are 6 equal angles inside the hexagon.

Each interior angle is 720º ÷ 6 = 120º

Work out the interior angle of a regular pentagon.

(just write the number) Work out the interior angle of a square.

(just write the number)

Work out the interior angle of a regular hexagon.

(just write the number) Work out the interior angle of a regular octagon.

(just write the number) Work out the interior angle of a regular nonagon.

(just write the number)

Work out the interior angle of a regular decagon.

(just write the number)

Work out the interior angle of a regular 12-sided polygon.

(just write the number)

Work out the interior angle of a regular 15-sided polygon.

(just write the number)

Work out the interior angle of a regular 18-sided polygon.

(just write the number)

Work out the interior angle of a regular heptagon to the nearest whole degree.

(just write the number) • Question 1

Work out the interior angle of a regular pentagon.

(just write the number) 108
• Question 2

Work out the interior angle of a square.

(just write the number)

90
• Question 3

Work out the interior angle of a regular hexagon.

(just write the number) 120
• Question 4

Work out the interior angle of a regular octagon.

(just write the number) 135
• Question 5

Work out the interior angle of a regular nonagon.

(just write the number)

140
• Question 6

Work out the interior angle of a regular decagon.

(just write the number)

144
• Question 7

Work out the interior angle of a regular 12-sided polygon.

(just write the number)

150
• Question 8

Work out the interior angle of a regular 15-sided polygon.

(just write the number)

156
• Question 9

Work out the interior angle of a regular 18-sided polygon.

(just write the number)

160
• Question 10

Work out the interior angle of a regular heptagon to the nearest whole degree.

(just write the number)  