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Interior Angles of Regular Polygons

In this worksheet, students calculate the interior angle of regular polygons.

'Interior Angles of Regular Polygons' worksheet

Key stage:  KS 2

Curriculum topic:   Maths and Numerical Reasoning

Curriculum subtopic:   2D Shapes: Triangles, Quadrilaterals and Polygons

Difficulty level:  

Worksheet Overview

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.

 

Answer

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)

 

 

CORRECT ANSWER
108
  • Question 2

Work out the interior angle of a square.

(just write the number)

CORRECT ANSWER
90
  • Question 3

Work out the interior angle of a regular hexagon.

(just write the number)

 

CORRECT ANSWER
120
  • Question 4

Work out the interior angle of a regular octagon.

(just write the number)

 

CORRECT ANSWER
135
  • Question 5

Work out the interior angle of a regular nonagon.

(just write the number)

CORRECT ANSWER
140
  • Question 6

Work out the interior angle of a regular decagon.

(just write the number)

 

 

CORRECT ANSWER
144
  • Question 7

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

(just write the number)

 

 

CORRECT ANSWER
150
  • Question 8

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

(just write the number)

 

 

CORRECT ANSWER
156
  • Question 9

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

(just write the number)

 

 

CORRECT ANSWER
160
  • Question 10

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

(just write the number)

 

 

CORRECT ANSWER
129
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