Question

find m∠opn. answer attempt 1 out of 2 m∠opn = °

Explanation:

Step1: Identify isosceles - triangle property

Since $OP = ON$ (the marks on the sides indicate they are equal), $\triangle{OPN}$ is an isosceles triangle. In an isosceles triangle, the base - angles are equal. Let $\angle{OPN}=\angle{ONP}$.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. In $\triangle{OPN}$, we know one angle $\angle{N} = 39^{\circ}$, and $\angle{OPN}=\angle{ONP}$. Let $x=\angle{OPN}=\angle{ONP}$. Then $x + x+39^{\circ}=180^{\circ}$, which simplifies to $2x=180^{\circ}- 39^{\circ}=141^{\circ}$.

Step3: Solve for $x$

Dividing both sides of the equation $2x = 141^{\circ}$ by 2, we get $x=\frac{141^{\circ}}{2}=70.5^{\circ}$.

Answer:

$70.5$