Question

in the figure, ( a parallel e ), ( m parallel n ), and ( mangle 3 = 112^circ ). what is the ( mangle 1 )? enter your answer in the box. \\( \square ^\circ \\)

Explanation:

Step1: Identify corresponding angles

Since $m \parallel n$, $\angle 3$ and $\angle 2$ are corresponding angles, so $m\angle 2 = m\angle 3 = 112^\circ$.

Step2: Identify supplementary angles

Since $\angle 1$ and $\angle 2$ are supplementary (form a linear pair), $m\angle 1 + m\angle 2 = 180^\circ$.

Step3: Calculate $m\angle 1$

Substitute $m\angle 2 = 112^\circ$ into the equation:
$m\angle 1 = 180^\circ - 112^\circ$

Answer:

$68$