△RST ∼ △XYZ.

Question

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

Answer 1

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

So, m∠X = 18° (corresponding to ∠R)
m∠Y = 75° (corresponding to ∠S)

To find m∠Z, we know that the sum of the angles in a triangle is 180°.

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