Question

geometry with data analysis ic qtr b young continuous learning center - credit bearing (tutor)
isosceles triangles
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 \\)?
17
102
90
6
instruction

Explanation:

Step1: Use the Vertex Angle of an Isosceles Triangle Theorem

Since \( \overline{ZY}\cong\overline{ZW}\) (given by the marks on the sides), \(\triangle ZWY\) is isosceles. And \(\overline{ZX}\) bisects \(\angle WZY\), so by the Isosceles Triangle Vertex - Angle Bisector Theorem, \(\overline{ZX}\perp\overline{WY}\). That means \(\angle YXZ = 90^{\circ}\).

Step2: Solve the equation for \(m\)

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

Answer:

\(17\)