Question

look at this diagram: if (overrightarrow{np}) and (overrightarrow{qs}) are parallel lines and (mangle nom = 61^{circ}), what is (mangle nor)?

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°. $\angle NOM$ and $\angle NOR$ form a linear - pair.

Step2: Set up the equation

Let $m\angle NOM = 61^{\circ}$ and $m\angle NOR=x$. Then $m\angle NOM + m\angle NOR=180^{\circ}$, so $61^{\circ}+x = 180^{\circ}$.

Step3: Solve for $x$

Subtract 61° from both sides of the equation: $x=180^{\circ}-61^{\circ}$.
$x = 119^{\circ}$.

Answer:

$119$