Angles in polygons

Use the interior angle sum formula

S = (n - 2) \times 180°

to find unknown angles in polygons and solve algebraic angle problems.

Worked examples

Finding the interior angle sum of a polygon

Straightforward

Problem

Find the sum of interior angles of a heptagon (7 sides).

Finding a missing interior angle in a polygon

Moderate

Problem

A hexagon has five interior angles of

125°

100°

110°

130°

and

95°

. Find the sixth angle.

Solving an algebraic angle problem in a polygon

Challenging

Problem

The interior angles of a pentagon are

x°

2x°

(x + 40)°

(x + 20)°

and

(x + 30)°

. Find

x

and state the largest angle.

Practise

Q1·Straightforward

Find the sum of interior angles of a hexagon.

Q2·Straightforward

Find the sum of interior angles of a pentagon.

Q3·Straightforward

Find the sum of interior angles of an octagon.

Q4·Straightforward

What is the sum of interior angles of a quadrilateral?

Q5·Moderate

A pentagon has interior angles of

100°

110°

95°

120°

and

x°

. Find

x

Q6·Moderate

Find the size of each interior angle of a regular hexagon.

Q7·Moderate

A quadrilateral has interior angles of

72°

95°

113°

and

x°

. Find

x

Q8·Moderate

Find the size of each interior angle of a regular octagon.

Q9·Challenging

Find the size of each exterior angle of a regular hexagon.

Q10·Challenging

The interior angles of a triangle are

x°

2x°

and

3x°

. Find

x

Q11·Challenging

Find the size of each exterior angle of a regular pentagon.

Q12·Challenging

The interior angles of a quadrilateral are

x°

(x + 20)°

(2x - 10)°

and

(x + 30)°

. Find

x