Question

look at this diagram: if $overleftrightarrow{hj}$ and $overleftrightarrow{km}$ are parallel lines and $mangle kli = 54^{circ}$, what is $mangle mli$?

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle KLI$ and $\angle MLI$ are a linear - pair of angles.

Step2: Use linear - pair property

The sum of angles in a linear pair is $180^{\circ}$. So, $m\angle KLI + m\angle MLI=180^{\circ}$.

Step3: Solve for $m\angle MLI$

Given $m\angle KLI = 54^{\circ}$, then $m\angle MLI=180^{\circ}-m\angle KLI$. Substitute $m\angle KLI = 54^{\circ}$ into the equation: $m\angle MLI = 180 - 54=126^{\circ}$.

Answer:

$126$