Question

In the diagram below, angle BAC = 34°.

Find the following angles, giving reasons for your answers.
a) angle ABC
b) angle BCA​

Answer 1

a) 90°

b) 56°

Explanation:

If we connect O with B to get two isosceles triangles: ΔAOB and ΔBOC

∠BOC= is central angle ans is twice as ∠BAC, so equals to 2*34°= 68°

Then ∠BCA= (180°- 68°)/2= 56°

∠ABC= ∠ABO+∠CBO= 34°+56°= 90°