Question

look at this diagram: if $overleftrightarrow{fh}$ and $overleftrightarrow{ik}$ are parallel lines and $mangle kjl = 54^{circ}$, what is $mangle ijl$?

Explanation:

Step1: Identify angle - type relationship

$\angle KJL$ and $\angle IJL$ are supplementary angles (linear - pair of angles).

Step2: Use the supplementary - angle property

The sum of supplementary angles is $180^{\circ}$. Let $m\angle IJL=x$. Then $x + m\angle KJL=180^{\circ}$.

Step3: Substitute the given value

Since $m\angle KJL = 54^{\circ}$, we have $x+54^{\circ}=180^{\circ}$.

Step4: Solve for $x$

$x=180^{\circ}- 54^{\circ}=126^{\circ}$.

Answer:

$126^{\circ}$