Question

question
in the diagram below, $overline{ab}paralleloverline{cd}$, $overline{ef}paralleloverline{gh}$, and $mangle ikl = 54^{circ}$. find $mangle ijl.
step angle reason
1 $mangle ikl = 54^{circ}$ given
$mangle ijl = 54^{circ}$ corresponding angles

Explanation:

Step1: Recall angle - property

When two parallel lines are intersected by a transversal, corresponding angles are equal. Here, due to the parallel - line relationships $\overline{AB}\parallel\overline{CD}$ and $\overline{EF}\parallel\overline{GH}$, $\angle IKL$ and $\angle IJL$ are corresponding angles.

Step2: Apply the property

Since $\angle IKL$ and $\angle IJL$ are corresponding angles and $m\angle IKL = 54^{\circ}$, then $m\angle IJL=m\angle IKL$.

Answer:

$54^{\circ}$