Question

look at this diagram: if $overleftrightarrow{km}$ and $overleftrightarrow{np}$ are parallel lines and $mangle mlo = 137.2^{circ}$, what is $mangle nol$? work it out

Explanation:

Step1: Identify angle - relationship

$\angle MLO$ and $\angle NOL$ are supplementary angles since $\overleftrightarrow{KM}$ and $\overleftrightarrow{NP}$ are parallel lines and they are same - side interior angles.

Step2: Use the supplementary - angle formula

The sum of supplementary angles is $180^{\circ}$. Let $m\angle NOL=x$. Then $x + m\angle MLO=180^{\circ}$. Given $m\angle MLO = 137.2^{\circ}$, we have $x=180^{\circ}-137.2^{\circ}$.

Step3: Calculate the angle measure

$x = 180 - 137.2=42.8^{\circ}$.

Answer:

$42.8$