Lines $m_{1}$, $m_{2}$, $l_{1}$ and $l_{2}$ are coplanar, and they are drawn such that $l_{1}$ is parallel to $l_{2}$, and $m_{2}$ is perpendicular to $l_{2}$. If the measure of angle 1 is 50 degrees, what is the measure in degrees of angle 2 in the figure below?

140 degrees

Step-by-step explanation:

Because m2 is perpendicular to l1, the bottom angle made from m2 and l1 is a right angle = 90 degrees.  The angle vertical to 1 = 50 degrees.  Thus, the angle made from both of these is equal to 140 degrees.  Because l1 is parallel to l2, <2 is congruent to this angle, and thus equals 140 degrees.  

Wow, that would be much easier if the angles were labeled.

Hope it helps <3

angle = 140 degrees

Step-by-step explanation:

Given:

All lines coplannar.

L1 || L2

m2 perpendicular to L1

angle 1 = 50 degrees

Solution

Refer to attached diagram

angle 4 = 90 degrees    ........... given

angle 3 = 180 - angle 4 - angle 1 = 180 - 90 - 50 = 40 degrees  .... angles on a line

angle 2 + angle 3 = 180 degrees  ............. sum interior angles between parallel lines L1 and L2

=>

angle 2 = 180 - angle 3 = 180 - 40 = 140 degrees.