m∠g=113° by the Vertical Angles Theorem
m∠k=125° by the Vertical Angles Theorem
Finding m∠h:
Because angle h is adjacent to angle g, and both angles lie on a straight line (180°), the sum of angle h and angle g is 180. We know the measure of angle g, so we can solve for h:
m∠g+m∠h=180°
Substitute in the measure of angle g:
(113)+m∠h=180
Subtract 113 from 180:
m∠h=180-113
m∠h=67°
Finding m∠m:
m∠k+ m∠m=180
Substitute the measurement in for m∠k:
(125)+m∠m=180
Subtract 125 from both sides:
m∠m=180-125
m∠m=55°