+385 Lines \($l$ and $k$\) are parallel to each other. \($m\angle A = 120^\circ$, and $m\angle C = 80^\circ$\). What is the number of degrees in \($m\angle B$\)?
+129852 Note that if we drew a perpedicular to both l and k we would have an (irregular) pentagon
Call the intersection points of this perpendicular to l and k , D and E, respectively
And since l and k are parallel then angle ADE = angle BED = 90°
And since the sum of the interior angles of a pentagon = 540°
So
angle A + angle C + angle B + angle D + angle E = 540
120 + 80 + angle B + 90 + 90 = 540 simplify
380 + angle B = 540 subtract 380 from both sides
angle B = 160°
