Question

find m∠mon. answer attempt 1 out of 2 m∠mon =

Explanation:

Step1: Identify isosceles triangle

Since \(OM = ON\) (indicated by the equal - side marks), \(\triangle OMN\) is an isosceles triangle. In an isosceles triangle, the base - angles are equal. So \(\angle OMN=\angle ONM = 57^{\circ}\).

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\angle MON=x\). Then \(x + 57^{\circ}+57^{\circ}=180^{\circ}\).

Step3: Solve for \(\angle MON\)

We can rewrite the equation as \(x=180^{\circ}-(57^{\circ}+57^{\circ})\). So \(x = 180^{\circ}-114^{\circ}=66^{\circ}\).

Answer:

\(66\)