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Angles and circles for SQA National 5 Maths

Angles and circles

This page covers the following topics:

1. Angle at the centre of the circle
2. Angles subtended by a semicircle
3. Angles in the same segment
4. Angles in cyclic quadrilaterals
5. Tangents and radii

The angle subtended at the centre of a circle is twice the angle subtended at the circumference.

Angle at the centre of the circle

The angle at the circumference of a semicircle is 90ยฐ.

Angles subtended by a semicircle

Angles in the same segment are equal.

Angles in the same segment

The sum of opposite angles in a cyclic quadrilateral is 180ยฐ.

Angles in cyclic quadrilaterals

A tangent to a circle is always perpendicular to the radius of that circle.

Tangents and radii

1

The angle subtended at the centre of a circle is 112ยฐ. What is the angle at the circumference?

56ยฐ

The angle subtended at the centre of a circle is 112ยฐ. What is the angle at the circumference?

2

What is a cyclic quadrilateral?

A cyclic quadrilateral is a 2D shape with four sides drawn inside a circle with every corner of the shape touching the circumference of the circle.

What is a cyclic quadrilateral?

3

What is the size of angle y?

270ยฐ

What is the size of angle y?

4

Do semicircles obey the rule that the angle at the centre of a circle is twice the angle subtended at the circumference of the centre?

yes

Do semicircles obey the rule that the angle at the centre of a circle is twice the angle subtended at the circumference of the centre?

5

Find the value of x.

30ยฐ

Find the value of x.

End of page

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