Question

Triangles PQR and XYZ are similar triangles. Which are the other two angle measures of triangle XYZ?

A. 35°
B. 70°
C. 75°
D. 95°
E. 105°

Answer 1

A, C

Explanation:

We are given that the triangles PQR and XYZ are similar.

Also, ∠ZXY = 70° and ∠PRQ = 35°.

Now, we know that when two triangles are similar, then the corresponding angles are same.

Therefore, ∠XZY = ∠PRQ = 35°

Now, in triangle XYZ, we have ∠XZY = 35° and ∠ZXY = 70°.

Since, we know that the sum of the angles of a triangle is 180°.

So, ∠XZY + ∠ZXY + ∠ZYX = 180°

i.e. 35° + 70° + ∠ZYX = 180°

i.e. ∠ZYX = 180° - ( 35° + 70° )

i.e. ∠ZYX = 180° - 105°

i.e. ∠ZYX = 75°

Hence, the other two angle measures of triangle XYZ are 35° and 75°.

Answer 2

Angle Z = Angle R = 35 degrees

Angle Y = 180-70-35 = 180-105 = 75

35 & 75 degrees