Question

1. what is m∠n?

Explanation:

Step1: Recall angle - sum property of a quadrilateral

The sum of the interior angles of a quadrilateral is 360°.

Step2: Identify known angles

We know that in the quadrilateral $OPMN$, $\angle O = 35^{\circ}$ and $\angle P = 180^{\circ}- 21^{\circ}=159^{\circ}$ (linear - pair of angles), $\angle M = 21^{\circ}$.

Step3: Calculate $\angle N$

Let $\angle N=x$. Then, using the angle - sum property of a quadrilateral: $x + 35^{\circ}+159^{\circ}+21^{\circ}=360^{\circ}$.
Simplify the left - hand side: $x+(35 + 159+21)^{\circ}=x + 215^{\circ}$.
So, $x=360^{\circ}-215^{\circ}$.
$x = 145^{\circ}$.

Answer:

$145^{\circ}$