Question

applying the vertex angle of an isosceles triangle theorem
\\( \overline { z x } \\) bisects \\( \angle w z y \\). if the measure of \\( \angle y x z \\) is \\( ( 6 m - 12 ) ^ { \circ } \\), what is
the value of \\( m \\)?

Explanation:

Step1: Use the Vertex Angle of an Isosceles Triangle Theorem

Since \( \overline{ZY}\cong\overline{ZW}\) (marked as equal in the isosceles triangle), and \( \overline{ZX}\) bisects \( \angle WZY\), then \( \overline{ZX}\perp\overline{WY}\) (by the Vertex Angle of an Isosceles Triangle Theorem which states that the bisector of the vertex - angle of an isosceles triangle is also the perpendicular bisector of the base). So, \( \angle YXZ = 90^{\circ}\).

Step2: Solve for \(m\)

Set up the equation \(6m−12 = 90\).
Add \(12\) to both sides: \(6m=90 + 12\), so \(6m=102\).
Divide both sides by \(6\): \(m=\frac{102}{6}=17\).

Answer:

\(17\)