Question

look at this diagram: if $overleftrightarrow{mo}$ and $overleftrightarrow{pr}$ are parallel lines and $mangle pqs = 65^{circ}$, what is $mangle pqn$?

Explanation:

Step1: Recall linear - pair property

A linear - pair of angles is supplementary, meaning the sum of the angles in a linear - pair is 180°. $\angle PQS$ and $\angle PQN$ form a linear - pair.

Step2: Set up the equation

Let $m\angle PQS = 65^{\circ}$ and $m\angle PQN=x$. Then $m\angle PQS + m\angle PQN=180^{\circ}$, so $65^{\circ}+x = 180^{\circ}$.

Step3: Solve for $x$

Subtract 65° from both sides of the equation: $x=180^{\circ}-65^{\circ}$.
$x = 115^{\circ}$

Answer:

$115$