Question

question
in \\( \triangle o p q, \overline{o p} \cong \overline{q o} \\) and \\( m \angle q = 12 ^ { \circ } \\). find \\( m \angle o \\).

Explanation:

Step1: Use the property of isosceles triangle

Since \(\overline{OP}\cong\overline{QO}\) in \(\triangle OPQ\), then \(\angle P=\angle Q\). Given \(m\angle Q = 12^{\circ}\), so \(m\angle P=12^{\circ}\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle O=x\). Then \(x + m\angle P+m\angle Q=180^{\circ}\). Substitute \(m\angle P = 12^{\circ}\) and \(m\angle Q = 12^{\circ}\) into the equation: \(x+12^{\circ}+12^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

\(x=180^{\circ}-(12^{\circ} + 12^{\circ})\)
\(x = 156^{\circ}\)

Answer:

\(156^{\circ}\)