Question

in the diagram below, \\( \overline { a b } \parallel \overline { c d } \\), \\( \overline { e f } \parallel \overline { g h } \\), and \\( m \angle i k l = 61 ^ { \circ } \\). find \\( m \angle a j g \\).

step
angle
reason
1
\\( m \angle i k l = 61 ^ { \circ } \\)
given
try \\( m \angle \square = \square ^ { \circ } \\)
select a reason

Explanation:

Step1: Find the measure of $\angle ILJ$

Since $\overline{EF}\parallel\overline{GH}$, and $\angle IKL$ and $\angle ILJ$ are corresponding angles.
By the Corresponding Angles Postulate, $\angle IKL=\angle ILJ = 61^{\circ}$.

Step2: Find the measure of $\angle AJG$

Since $\angle AJG$ and $\angle ILJ$ are vertical angles.
By the Vertical Angles Theorem, $\angle AJG=\angle ILJ$.
So, $m\angle AJG = 61^{\circ}$.

Answer:

$m\angle AJG = 61^{\circ}$