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°

Explanation:

Step1: Use triangle angle sum property

The sum of angles in a triangle is $180^\circ$, so $m\angle X + m\angle Y + m\angle Z = 180^\circ$.

Step2: Substitute the given inequality

Given $m\angle Z > m\angle X + m\angle Y$, replace $m\angle Z$ with $180^\circ - (m\angle X + m\angle Y)$:
$180^\circ - (m\angle X + m\angle Y) > m\angle X + m\angle Y$.

Step3: Solve for $m\angle X + m\angle Y$

Add $(m\angle X + m\angle Y)$ to both sides: $180^\circ > 2(m\angle X + m\angle Y)$.
Divide by 2: $90^\circ > m\angle X + m\angle Y$.

Answer:

D. $m\angle X + m\angle Y < 90^\circ$