Question

complete the table below

measure	justification
m∠2 =
m∠3 =
m∠4 =

Explanation:

Step1: Identify vertical - angle property

Vertical angles are equal. $\angle1$ and the given $67^{\circ}$ angle are vertical angles. So $m\angle1 = 67^{\circ}$.

Step2: Identify corresponding - angle property

$\angle2$ and the given $67^{\circ}$ angle are corresponding angles. So $m\angle2=67^{\circ}$.

Step3: Identify linear - pair property

$\angle2$ and $\angle3$ form a linear pair. Since the sum of angles in a linear pair is $180^{\circ}$, $m\angle3 = 180 - 67=113^{\circ}$.

Step4: Identify vertical - angle property for $\angle4$

$\angle3$ and $\angle4$ are vertical angles. So $m\angle4 = 113^{\circ}$.

Answer:

$m\angle1 = 67^{\circ}$
$m\angle2 = 67^{\circ}$
$m\angle3 = 113^{\circ}$
$m\angle4 = 113^{\circ}$