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°

Solution:

Given, XYZ is a triangle.

We have to find the option that is true about △XYZ.

By angle sum property of a triangle,

The sum of all the interior angles of a triangle is always equal to 180°.

So, ∠X + ∠Y + ∠Z = 180°

Given, m∠Z > m∠X + m∠Y.

This implies that ∠Z is greater than the sum of the angles ∠X and ∠Y.

So, ∠X + ∠Y must be less than 90°.

Therefore, ∠X + ∠Y < 90°

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

Summary:

In triangle XYZ, m∠Z > m∠X + m∠Y. m∠X + m∠Y < 90°must be true about △XYZ.