Question

in △opq, \overline{op} \cong \overline{qo} and m∠q = 12°. find m∠o.

Explanation:

Step1: Identify the triangle type

Since \(\overline{OP} \cong \overline{QO}\), \(\triangle OPQ\) is isosceles with \(\angle P \cong \angle Q\).
So \(m\angle P = m\angle Q = 12^\circ\).

Step2: Use triangle angle sum

The sum of angles in a triangle is \(180^\circ\). Let \(m\angle O = x\). Then:
\(x + 12^\circ + 12^\circ = 180^\circ\)

Step3: Solve for \(x\)

\(x + 24^\circ = 180^\circ\)
\(x = 180^\circ - 24^\circ = 156^\circ\)

Answer:

\(156^\circ\)