△RST ∼ △XYZ. m∠R = 18°, m∠S = 75°. What are the measures of angles X, Y, and Z?
Since △RST ∼ △XYZ, we know that the corresponding angles are equal. Therefore, we have:
m∠R = m∠X
m∠S = m∠Y
m∠T = m∠Z
We are given that m∠R = 18° and m∠S = 75°.
Therefore:
m∠X = 18° (corresponding angle to ∠R)
m∠Y = 75° (corresponding angle to ∠S)
To find the measure of ∠Z, we can use the fact 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 = 87°
Therefore, the measures of angles X, Y, and Z are 18°, 75°, and 87°, respectively.