△XYZ∼△RST. m∠R=18, m∠S=75. What is the measure of angles X,Y,AND Z

Answer 1

Since △XYZ∼△RST, the corresponding angles are congruent.

Given:
m∠R = 18°
m∠S = 75°

We can conclude that:
m∠X = 18° (corresponding angle to ∠R)
m∠Y = 75° (corresponding angle to ∠S)

To find the measure of angle Z, we need to consider the fact that the sum of angles in a triangle is always 180°.

Therefore, we can add the measures of ∠X and ∠Y, and then subtract the sum from 180° to find ∠Z:

m∠Z = 180° - (m∠X + m∠Y)
m∠Z = 180° - (18° + 75°)
m∠Z = 180° - 93°
m∠Z = 87°

So, the measure of angle Z is 87°.