ABDE is a cyclic quadrilateral - Edexcel - GCSE Maths - Question 16 - 2022 - Paper 3

Let the size of angle BCD be denoted as x. Then the size of angle EAB can be expressed as 2x.

Since EAB and BCD lie within the same cyclic quadrilateral, we can apply the property of angles in cyclic quadrilaterals, which states that opposite angles sum to 180°:

$EAB + BCD + DBC = 180°$

Substituting the known angles, we have:

$2x + x + 60° = 180°$

This simplifies to:

$3x + 60° = 180°$

Subtracting 60° from both sides gives:

$3x = 120°$

Dividing both sides by 3 results in:

$x = 40°$

Thus, the size of angle BCD is 40°.