Answer:
The angles are, x = 64 degrees, y = 64 degrees, z = 20 degrees
Explanation:
Since ABD is an isosceles triangle and since AB = AD
Angle x must equal angle y so, x = y
and since the sum of all angles in a triangle is 180 we get,
180 = x + y + 52
180 = x + x + 52
180 - 52 = 2x
128 = 2x
x = 128/2
x =64 degrees
and hence y = 64 degrees (since x = y)
For Triangle ABC,
we know that angle x = 64, the angle at point C is 44
and the angle at point A is 52 + z
Again, using the sum of angles of a triangle, we get,
180 = 64 + 44 + (52 +z)
180 = 64 + 44 + 52 + z
180 = 160 + z
z = 180 - 160
z = 20 degrees