Question

question
in △mno, overline{om} cong overline{no} and m∠n = 17°. find m∠m.

Explanation:

Step1: Determine the type of triangle

Since $\overline{OM}\cong\overline{NO}$, $\triangle MNO$ is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. So, $\angle M=\angle O$.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. Let $m\angle M = x$ and $m\angle O=x$ (because $\angle M\cong\angle O$), and $m\angle N = 17^{\circ}$. Then, by the angle - sum property of a triangle:

$$x + x+17^{\circ}=180^{\circ}$$

$$2x=180^{\circ}- 17^{\circ}$$

$$2x = 163^{\circ}$$

$$x=\frac{163^{\circ}}{2}=81.5^{\circ}$$

Answer:

$m\angle M = 81.5^{\circ}$