Question

answer attempt 1 out of 2
m∠mon =
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Explanation:

Step1: Identify isosceles triangle

The triangle has two equal - length sides, so it is isosceles. In an isosceles triangle, the base - angles are equal.

Step2: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. Let $\angle MON=x$. Since the base - angles are equal and one non - base angle $\angle N = 52^{\circ}$, and the other two angles are equal. Let the base - angles be $\angle M=\angle O$.
We know that $x + x+52^{\circ}=180^{\circ}$.
Combining like terms gives $2x=180^{\circ}- 52^{\circ}$.
$2x = 128^{\circ}$.
Dividing both sides by 2: $x=\frac{128^{\circ}}{2}=64^{\circ}$.

Answer:

$64$