Question

if m <2 = 75, find the measure of the remaining angles.
drawing not to scale
m <1 =
m <3 =
m <4 =

Explanation:

Step1: Vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle2$ are vertical - angles. So, $m\angle1=m\angle2$.
$m\angle1 = 75$

Step2: Supplementary - angle property

$\angle1$ and $\angle4$ are supplementary (linear pair), so $m\angle1 + m\angle4=180$.
$m\angle4=180 - m\angle1=180 - 75 = 105$

Step3: Vertical - angle property

$\angle3$ and $\angle4$ are vertical - angles. So, $m\angle3=m\angle4$.
$m\angle3 = 105$

Answer:

$m\angle1 = 75$
$m\angle3 = 105$
$m\angle4 = 105$