Question

What is m∠1
, in degrees, in the figure below?

Two intersecting lines that form 4 angles. Angle one is adjacent to angle two and together form a straight angle. Angle two is vertical to the angle labeled X minus 30 degrees, which is adjacent to the angle labeled 2 X plus 15 degrees. Together, these two angles also form a straight angle.

Answer 1

Let X − 30 and 2X + 15 be a linear pair, so
(X − 30) + (2X + 15) = 180
3X − 15 = 180 → 3X = 195 → X = 65.

Then angle 2 = X − 30 = 65 − 30 = 35° (vertical angles are equal), and angle 1 is supplementary to angle 2:
m∠1 = 180 − 35 = 145°.

Answer: 145°.