in triangle xyz, ( mangle z>mangle x + mangle y ). which must be true about ( \triangle xyz )?\n( mangle x +…

in triangle xyz, ( mangle z>mangle x + mangle y ). which must be true about ( \triangle xyz )?\n( mangle x + mangle z<90^{circ} )\n( mangle y>90^{circ} )\n( angle x ) and ( angle y ) are complementary\n( mangle x + mangle y<90^{circ} )

in triangle xyz, ( mangle z>mangle x + mangle y ). which must be true about ( \triangle xyz )?\n( mangle x + mangle z<90^{circ} )\n( mangle y>90^{circ} )\n( angle x ) and ( angle y ) are complementary\n( mangle x + mangle y<90^{circ} )

Answer

Explanation:

Step1: Use the triangle - angle sum theorem

In any triangle ( \triangle XYZ), (m\angle X + m\angle Y+m\angle Z=180^{\circ}), so (m\angle X + m\angle Y = 180^{\circ}-m\angle Z).

Step2: Substitute into the given inequality

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

Step3: Solve the inequality for (m\angle Z)

Add (m\angle Z) to both sides: (2m\angle Z>180^{\circ}). Then divide both sides by 2: (m\angle Z > 90^{\circ}). Since (m\angle X + m\angle Y+m\angle Z=180^{\circ}), if (m\angle Z>90^{\circ}), then (m\angle X + m\angle Y=180^{\circ}-m\angle Z<90^{\circ}).

Answer:

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