Question

question
in \\( \triangle o p q, \overline{q o} \cong \overline{p q} \\) and \\( m \angle p = 59 ^ { \circ } \\). find \\( m \angle q \\).

Explanation:

Step1: Identify triangle type

Since \(\overline{QO} \cong \overline{PQ}\), \(\triangle OPQ\) is isosceles with \(\angle P \cong \angle O\). So \(m\angle O = m\angle P = 59^\circ\).

Step2: Sum of angles in triangle

The sum of angles in a triangle is \(180^\circ\). Let \(m\angle Q = x\). Then \(x + 59^\circ + 59^\circ = 180^\circ\).

Step3: Solve for \(m\angle Q\)

\(x = 180^\circ - 59^\circ - 59^\circ = 62^\circ\).

Answer:

\(62^\circ\)