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…

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

Explanation:

Step1: Recall triangle - angle sum property

The sum of the interior angles of a triangle is (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

We know that (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}).

Answer:

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