The opposite angles of a cyclic quadrilateral sum to 180° | Maths

Starter quiz

Calculate the size of angle $a$ °.

26°

32° ✓

58°

64°

128°
The size of the angle labelled $b$ ° is ______°.

'79' ✓
The size of the angle labelled $c$ ° is ______°.

'56' ✓
The size of the angle labelled $d$ ° is ______°.

'50' ✓
∠PEF is subtended by the chord PF. ∠PFE is subtended by the chord PE. Find ∠EPD (in degrees).

'92' ✓
Calculate the size of angle $h$ °.

'39' ✓

Exit quiz

The size of the angle labelled $a$ ° is ______°.

'170' ✓
Find the size of angle $b$ °.

85°

90°

95° ✓

170°

190°
Find the size of angle $c$ °.

83° ✓

87°

93°

97°

Not enough information.
The size of the angle labelled $d$ ° is ______°.

'90' ✓
The size of the angle labelled $e$ ° is ______°.

'32' ✓
Find the size of angle $g$ ° (in degrees).

'90' ✓

Worksheet

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Lesson Details

Key learning points

A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments
Theorems can be thought of as puzzles to solve, you are showing how to find a result
In order to use this theorem, you may need to draw a diagram or add more information to an existing one

Common misconception

Pupils may conflate cyclic quadrilaterals with cases of "the angle at the centre of a circle is twice the angle at the circumference" theorem, when the angle at the centre is a reflex angle.

While the two diagrams may look similar at a glance, pay extra attention to whether all four points of the quadrilateral are on the circumference or if one of the points is in the centre.

Keywords

Cyclic quadrilateral - A cyclic quadrilateral is a quadrilateral where all four of its vertices lie on a single circle.