Question △RST ∼ △XYZ. m∠R = 18° , m∠S = 75° . What are the measures of angles X , Y , and Z ?

Answer 1

Since △RST ∼ △XYZ, the corresponding angles will be congruent.

Therefore, m∠X = 18° and m∠Y = 75°.

Since the sum of angles in a triangle is 180°, we can find m∠Z by subtracting the other two angles from 180°.

m∠Z = 180° - m∠X - m∠Y
m∠Z = 180° - 18° - 75°
m∠Z = 87°

So, the measures of angles X, Y, and Z are 18°, 75°, and 87° respectively.