Question

look at this diagram:
if (overleftrightarrow{gi}) and (overleftrightarrow{jl}) are parallel lines and (mangle lkm = 46^{circ}), what is (mangle jkm?)

Explanation:

Step1: Identify the relationship between angles

$\angle JKM$ and $\angle LKM$ 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 $\alpha=\angle JKM$ and $\beta = \angle LKM$. We know that $\beta=46^{\circ}$.
So, $\angle JKM+46^{\circ}=180^{\circ}$.

Step3: Solve for $\angle JKM$

Subtract $46^{\circ}$ from both sides of the equation: $\angle JKM=180^{\circ}- 46^{\circ}$.
$180 - 46=134$.

Answer:

$134$