in triangle xyz, m∠z > m∠x + m∠y. which must be true about △xyz?\no m∠x + m∠z < 90°\no m∠y > 90°\no ∠x and…

in triangle xyz, m∠z > m∠x + m∠y. which must be true about △xyz?\no m∠x + m∠z < 90°\no m∠y > 90°\no ∠x and ∠y are complementary\no m∠x + m∠y < 90°

in triangle xyz, m∠z > m∠x + m∠y. which must be true about △xyz?\no m∠x + m∠z < 90°\no m∠y > 90°\no ∠x and ∠y are complementary\no m∠x + m∠y < 90°

Answer

Answer:

D. (m\angle X + m\angle Y<90^{\circ})

Explanation:

Step1: Record the angle - sum property of a triangle

We know that for (\triangle XYZ), (m\angle X + m\angle Y+m\angle Z = 180^{\circ}), so (m\angle Z=180^{\circ}-(m\angle X + m\angle Y)).

Step2: Use the given inequality

Given (m\angle Z>m\angle X + m\angle Y). Substitute (m\angle Z = 180^{\circ}-(m\angle X + m\angle Y)) into the inequality: (180^{\circ}-(m\angle X + m\angle Y)>m\angle X + m\angle Y).

Step3: Solve the inequality

Add ((m\angle X + m\angle Y)) to both sides: (180^{\circ}>2(m\angle X + m\angle Y)). Then divide both sides by 2: (m\angle X + m\angle Y < 90^{\circ}).