Question

look at this diagram: if (overleftrightarrow{ik}) and (overleftrightarrow{ln}) are parallel lines and (mangle nmj = 118.3^{circ}), what is (mangle ijm?)

Explanation:

Step1: Identify angle - relationship

$\angle NMJ$ and $\angle IJM$ are supplementary angles since $\overleftrightarrow{IK}$ and $\overleftrightarrow{LN}$ are parallel lines and $OH$ is a transversal.

Step2: Use the supplementary - angle formula

The sum of supplementary angles is $180^{\circ}$. Let $m\angle IJM = x$. Then $m\angle NMJ+x = 180^{\circ}$. Given $m\angle NMJ = 118.3^{\circ}$, we have $x=180^{\circ}-m\angle NMJ$.

Step3: Calculate the angle measure

$x = 180 - 118.3=61.7^{\circ}$.

Answer:

$61.7$