Question

question
in △nop, $overline{op}congoverline{no}$ and m∠o = 57°. find m∠n.

Explanation:

Step1: Identify the triangle type

Since $\overline{OP}\cong\overline{NO}$, $\triangle NOP$ is an isosceles triangle. In an isosceles triangle, the base - angles are equal. Let $\angle N=\angle P = x$.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. So, $m\angle N + m\angle O+m\angle P=180^{\circ}$. Substituting $m\angle N = x$, $m\angle O = 57^{\circ}$, and $m\angle P = x$ into the equation, we get $x + 57^{\circ}+x=180^{\circ}$.

Step3: Solve the equation for $x$

Combining like terms, we have $2x+57^{\circ}=180^{\circ}$. Subtract $57^{\circ}$ from both sides: $2x=180^{\circ}- 57^{\circ}=123^{\circ}$. Then divide both sides by 2: $x=\frac{123^{\circ}}{2}=61.5^{\circ}$.

Answer:

$61.5^{\circ}$