Question

Look at triangle ABC.

ABD is an isosceles triangle where AB = AD.
A
B
X
52°
Z
D
Work out the sizes of angles x, y and z.
44
C

Answer 1

ABD is an isosceles triangle, so the base angles are congruent.

52° + (2x)° = 180°

2x = 128, so x = y = 64°.

BDA and ADC are supplementary angles, so angle ADC measures 116°. It follows that z = 20°.