Interior angles of a regular polygon | GCSE / IGCSE Maths

Geometry and measuresKey Stage 3

Use polygon angle facts to find missing values.

All sides and all interior angles of a regular polygon are equal.
One interior angle is .

Example 1

Find angle in this regular 5-sided polygon.

First find the interior-angle sum.

All interior angles of a regular polygon are equal.

First find the interior-angle sum.

All interior angles of a regular polygon are equal.

Example 2

Find angle in this regular 6-sided polygon.

First find the interior-angle sum.

All interior angles of a regular polygon are equal.

First find the interior-angle sum.

All interior angles of a regular polygon are equal.

Your turn

Question 1

Find angle in this regular 8-sided polygon.

Check answer

First find the interior-angle sum.

All interior angles of a regular polygon are equal.

First find the interior-angle sum.

All interior angles of a regular polygon are equal.

Question 2

Find angle in this regular 9-sided polygon.

Check answer

First find the interior-angle sum.

All interior angles of a regular polygon are equal.

First find the interior-angle sum.

All interior angles of a regular polygon are equal.

Question 3

Find angle in this regular 10-sided polygon.

Check answer

First find the interior-angle sum.

All interior angles of a regular polygon are equal.

First find the interior-angle sum.

All interior angles of a regular polygon are equal.

Question 4

Find angle in this regular 12-sided polygon.

Check answer

First find the interior-angle sum.

All interior angles of a regular polygon are equal.

First find the interior-angle sum.

All interior angles of a regular polygon are equal.

Question 5

Find angle in this regular 5-sided polygon.

Check answer

First find the interior-angle sum.

All interior angles of a regular polygon are equal.

First find the interior-angle sum.

All interior angles of a regular polygon are equal.