Question

zx bisects ∠wzy. if the measure of ∠yxz is (6m − 12)°, what is the value of m?
○ 6
○ 17
○ 90
○ 102

Explanation:

Step1: Identify triangle properties

From the diagram, \( ZY = ZW \) (marked with ticks) and \( \overline{ZX} \) bisects \( \angle WZY \). So, by the Angle - Bisector and Isosceles Triangle property, \( \overline{ZX} \perp \overline{WY} \), so \( \angle YXZ = 90^{\circ} \).

Step2: Set up the equation

We know that \( \angle YXZ=(6m - 12)^{\circ} \) and \( \angle YXZ = 90^{\circ} \). So we set up the equation:
\( 6m-12 = 90 \)

Step3: Solve for m

Add 12 to both sides of the equation:
\( 6m=90 + 12=102 \)
Divide both sides by 6:
\( m=\frac{102}{6}=17 \)

Answer:

17