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SQA National 5 Maths Angles and circles

Angles and circles

This page covers the following topics:

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 90Β°.

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 180Β°.

Angles in cyclic quadrilaterals

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

Tangents and radii

1

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The angle at the centre of a circle is 84Β°. What is the angle at the circumference?

SQA National 5 Maths Angles and circles The angle at the centre of a circle is 84Β°. What is the angle at the circumference?
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2

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Find the value of x.

SQA National 5 Maths Angles and circles Find the value of x.
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3

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A circle is cut in half by a straight line to form a semicircle. What is therefore the size of the angle formed at the centre?

SQA National 5 Maths Angles and circles A circle is cut in half by a straight line to form a semicircle. What is therefore the size of the angle formed at the centre?
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4

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Find the size of angle y.

SQA National 5 Maths Angles and circles Find the size of angle y.
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5

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Calculate the angles x and y.

SQA National 5 Maths Angles and circles Calculate the angles x and y.
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6

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What is the sum of all angles in a cyclic quadrilateral?

SQA National 5 Maths Angles and circles What is the sum of all angles in a cyclic quadrilateral?
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7

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What is the size of angle x?

SQA National 5 Maths Angles and circles What is the size of angle x?
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8

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Calculate the value of p.

SQA National 5 Maths Angles and circles Calculate the value of p.
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9

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The surface area of a circle is doubled. What happens to the angle between the tangent and radius on the new circle?

SQA National 5 Maths Angles and circles The surface area of a circle is doubled. What happens to the angle between the tangent and radius on the new circle?
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10

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What is the size of angle y?

SQA National 5 Maths Angles and circles What is the size of angle y?
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