# StudySquare

# Angles in shapes for AQA GCSE Maths

This page covers the following topics:

1. Sum of angles in a triangle

2. Sum of angles in a square

3. Sum of angles and inner angles

4. Sum of angles and outer angles

The sum of interior angles in a triangle is 180°. If the side of a triangle is extended, an angle is created outside the triangle called an exterior angle.

A square has 4 interior angles, all of equal size 90°.

The sum of interior angles in a polygon can be found by dividing the polygon into a number of triangles.

The exterior angles of a polygon can be found by extending the sides of the polygon to form an angle outside the shape.

# 1

Calculate the sum of interior angles in a pentagon.

540°

# 2

Calculate the size of the exterior angles in the shape shown and hence, calculate the size of the interior angles.

exterior angle = 72°

interior angle = 108°

# 3

If x is the number of sides in a polygon, write a formula that can be used to find the sum of interior angles in the polygon.

180º(x − 2)

# 4

Find the size of angle x.

38°

# 5

Calculate the sum of the interior angles in the shape shown.

1080°

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