△RST ∼ △XYZ.%0D%0A△%0D%0A%0D%0A%0D%0A%0D%0A %0D%0A∼%0D%0A %0D%0A△%0D%0A%0D%0A%0D%0A%0D%0A.%0D%0A m∠R = 18°%0D%0A%0D%0A∠%0D%0A%0D%0A %0D%0A=%0D%0A %0D%0A18%0D%0A°%0D%0A, m∠S = 75°%0D%0A%0D%0A∠%0D%0A%0D%0A %0D%0A=%0D%0A %0D%0A75%0D%0A°%0D%0A. What are the measures of angles X%0D%0A%0D%0A, Y%0D%0A%0D%0A, and Z%0D%0A%0D%0A?
To solve this problem, we can use the fact that corresponding angles of similar triangles are congruent.
Since ∠R is congruent to ∠X, we know that m∠X is also 18°.
Similarly, since ∠S is congruent to ∠Y, we know that m∠Y is 75°.
Finally, since the sum of the angles in any triangle is always 180°, we can subtract the measures of ∠R, ∠X, and ∠Y from 180° to find the measure of ∠Z.
180° - 18° - 75° = 87°
Therefore, the measures of angles X, Y, and Z are:
m∠X = 18°
m∠Y = 75°
m∠Z = 87°