Answer:
(d) m∠X + m∠Y < 90°
Step-by-step explanation:
You want to know what must be true of the angles in ∆XYZ, given Z > X + Y.
We know the sum of angles in the triangle is 180°. The given conditions let us write two expressions for Z:
Z > X + Y
Z = 180° -(X + Y)
Substituting for Z, we have ...
180° -(X +Y) > X +Y
180° > 2(X +Y) . . . . . . . . . . add (X +Y)
Dividing by 2 gives ...
X + Y < 90° . . . . . . . matches choice D