Answer:
x = 75°; y = 75°; z = 30°
Step-by-step explanation:
I am using points A and B as vertices of the triangle.
From the figure, we see that segments BC and AC are congruent. Since they are sides of triangle ABC, that makes their opposite angles, A and B, congruent angles.
m<A = m<B
We are given m<B = 75°,
so m<A = m<B = 75°
In a triangle, the sum of the measures of the interior angles is 180°.
m<A + m<B + z = 180°
Use substitution for angles A and B:
75° + 75° + z = 180°
z = 30°
Lines AB and DE are shown to be parallel. That makes alternate interior angles congruent. Lines AC and BC are transversals to the parallel lines.
m<A = y
y = m<A = 75°
m<B = x
x = m<B = 75°
Answer: x = 75°; y = 75°; z = 30°
