Question

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

Explanation:

Step1: Identify triangle properties

The triangle has equal sides (marked with ticks), so it's isosceles: \(ZW = ZY\), \(ZX = ZX\), and \(\angle WZX = \angle YZX\) (angle bisector). Thus, \(\triangle ZWX \cong \triangle ZYX\) (SAS).

Step2: Set up equation for angle

\(\angle YXZ\) is a right angle? No, wait—since \(\triangle ZWX \cong \triangle ZYX\), \(\angle ZXY = \angle ZXW\). If they are right angles (common in such diagrams), then \(6m - 12 = 90\).

Step3: Solve for m

\(6m = 90 + 12 = 102\) → \(m = \frac{102}{6} = 17\).

Answer:

B. 17