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Angles in shapes for AQA GCSE Maths

Angles in shapes

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 180ยฐ. If the side of a triangle is extended, an angle is created outside the triangle called an exterior angle.

Sum of angles in a triangle

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

Sum of angles in a square

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

Sum of angles and inner angles

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

Sum of angles and outer angles

1

Calculate the sum of interior angles in a pentagon.

540ยฐ

Calculate the sum of interior angles in a pentagon.

2

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

exterior angle = 72ยฐ
interior angle = 108ยฐ

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

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.

180ยบ(x โˆ’ 2)

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.

4

Find the size of angle x.

38ยฐ

Find the size of angle x.

5

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

1080ยฐ

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

End of page

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