Question

if \\( \overline { t w } \cong \overline { v w } \\), \\( m \angle t u w = 3 p \\), and \\( m \angle v u w = p + 36 ^ { \circ } \\), what is the value of \\( p \\)?

Explanation:

Step1: Use the Angle Bisector Theorem

Since \( \overline{TW}\cong\overline{VW}\), \(WU\) is the angle bisector of \( \angle VUT\). So \(m\angle TUW = m\angle VUW\).

Step2: Set up the equation

We have \(3p=p + 36^{\circ}\).
Subtract \(p\) from both sides: \(3p-p=p + 36^{\circ}-p\).
So \(2p=36^{\circ}\).
Divide both sides by 2: \(p=\frac{36^{\circ}}{2}\).

Answer:

\(18\)