Question

In triangle XYZ, m∠Z > m∠X + m∠Y. Which must be true about △XYZ?

m∠X + m∠Z < 90°
m∠Y > 90°
∠X and∠Y are complementary
m∠X + m∠Y < 90°

Answer 1

Use the triangle angle sum: X + Y + Z = 180°. Given Z > X + Y, replace X + Y with 180 − Z:

Z > 180 − Z ⇒ 2Z > 180 ⇒ Z > 90°.

Thus X + Y = 180 − Z < 90°. So m∠X + m∠Y < 90° (choice 4).