Question

look at this diagram: if (overleftrightarrow{ik}) and (overleftrightarrow{ln}) are parallel lines and (mangle kjm = 48^{circ}), what is (mangle ijm?)

Explanation:

Step1: Identify the relationship between angles

$\angle KJM$ and $\angle IJM$ are supplementary angles (they form a linear - pair).

Step2: Use the supplementary - angle formula

If two angles $\alpha$ and $\beta$ are supplementary, then $\alpha+\beta = 180^{\circ}$. Let $\alpha=\angle KJM = 48^{\circ}$ and $\beta=\angle IJM$.
We have the equation $48^{\circ}+\angle IJM=180^{\circ}$.

Step3: Solve for $\angle IJM$

Subtract $48^{\circ}$ from both sides of the equation:
$\angle IJM=180^{\circ}-48^{\circ}$.

Answer:

$132$