Edexcel IGCSE Math B 6.L Cyclic quadrilaterals Question Bank

Practise finding angles in cyclic quadrilaterals by using the relationship between opposite angles in a circle.

Exam points

calculate a missing cyclic quadrilateral angle from the opposite angle summing to 180°
give the geometric reason clearly when using opposite angles in a cyclic quadrilateral

[Maximum number: 2]

Diagram NOT accurately drawn

In the diagram, A, B, C and D are points on a circle, centre O. $\angle C B O=62^{\circ}$ and $\angle B C D=126^{\circ}$

Find the size, in degrees, of $\angle B A D$ .

Give a reason for your answer.

\angle B A D=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .

CFDE is cyclic, so opposite angles sum to $180^\circ$ :
$\angle CDE=180^\circ-126^\circ=54^\circ.$

Answer: $54^\circ$ .

Marks: B1.

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