Maths

Angles - Foundation

Simple angle facts

There are 360° in a complete turn. So in half a turn there are 180°, and in a quarter of a turn 90°.

three different angles

We sometimes call a quarter of a turn a right angle, and mark it with a square.

We can use these facts to solve simple problems. Here are some examples:

Question
image: angle split four ways

Find angle a in this diagram:

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Answer

The answer is 110°.

All the angles add up to 360° (a complete turn).

So a = 360° - 60° - 100° - 90° = 110°.

Remember that a right angle (90°) can be marked with a square.

Question
image: angle split three ways

Find angle b in this diagram.

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Answer

The answer is 100°.

The angles make a straight line (half a turn).

So b = 180° - 50° - 30° = 100°.

Question
image: an angle

Find angle c in this diagram.

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Answer

The answer is 70°.

The two angles make a right angle.

So c = 90° - 20° = 70°

Different types of angle

For your exam, you will need to know the following types of angle:

image: an angle

Any angle that is less than 90° is called an acute angle.

image: an angle

Any angle which is between 90° and 180° is called an obtuse angle.

image: an angle

Any angle that is between 180° and 360° is called a reflex angle.

You also need to remember that the angles in a triangle add up to 180°, and that the angles in a quadrilateral add up to 360°.

image: traingle and trapezium

p + q + r = 180°         w + x + y + Z = 360°

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