Question

Could anyone please help me with this question? thanks

Answer 1

AB = AC, so this is an isosceles triangle, then angle B=angle C =66⁰.
m∠BAD = m∠CAD, so AD is a bisector. 
In an isosceles triangle, bisector is also median and height.
So AD is perpendicular bisector.
So angle x = 90⁰. 

In triangle ABC
m∠A+m∠B+m∠C=180⁰
m∠A+66+66=180
m∠A=180-66-66=48⁰

m∠A=48⁰
AD is a bisector of A, so y=m∠A/2=48⁰/2=24⁰


x=90⁰, y=24⁰
Answer is A