Question

in the diagram below, \\(\overline{ab} \parallel \overline{cd}\\), \\(\overline{ef} \parallel \overline{gh}\\), and \\(m\angle ikl = 57^\circ\\). find \\(m\angle ajg\\).

you may assume lines that appear straight are straight, but the figure is not otherwise drawn to scale.

answer attempt 1 out of 2
\\(m\angle ajg = \square^\circ\\)

Explanation:

Step1: Identify corresponding angles

Since $\overline{EF} \parallel \overline{GH}$ and $\overline{CD}$ is a transversal, $\angle IKL$ and $\angle JLC$ are corresponding angles, so $m\angle JLC = m\angle IKL = 57^\circ$.

Step2: Identify alternate interior angles

Since $\overline{AB} \parallel \overline{CD}$ and $\overline{GH}$ is a transversal, $\angle AJG$ and $\angle JLC$ are alternate interior angles, so $m\angle AJG = m\angle JLC$.

Step3: Substitute the known angle value

Substitute $m\angle JLC = 57^\circ$ into the equation from Step 2.

Answer:

$57$