Question

m∠ikl=63°, find m∠ajg.
step
angle
reason
1
m∠ikl=63°
given
try m∠□=□°
select a reason
you may assume lines that appear straight are straight, but the figure is not otherwise

Explanation:

Step1: Find the measure of $\angle ILJ$

Since $EF\parallel GH$, and $\angle IKL$ and $\angle ILJ$ are corresponding angles.
By the Corresponding Angles Theorem, if two parallel lines are cut by a transversal, then corresponding angles are congruent.
So, $m\angle ILJ = 63^{\circ}$

Step2: Find the measure of $\angle AJG$

Since $AB\parallel CD$, and $\angle AJG$ and $\angle ILJ$ are alternate - interior angles.
By the Alternate - Interior Angles Theorem, if two parallel lines are cut by a transversal, then alternate - interior angles are congruent.
So, $m\angle AJG=63^{\circ}$

Answer:

$m\angle AJG = 63^{\circ}$