Question

3 lines are shown. A line with points M, H, K intersects with a line with points J, H, L at point H. Another line extends from point H to point N in between angle K, H, J. Angle M H L is (3 x + 20) degrees, angle K H N is (x + 25) degrees, and angle J H N is (x + 20) degrees.
What is the measure of AngleJHN?

25°
45°
50°
95°

Answer 1

Let angle K H J = angle M H L = 3x + 20 (opposite rays give the same angle). Since N lies between K and J,
angle KHN + angle JHN = angle KHJ, so (x+25) + (x+20) = 3x+20.
Thus 2x + 45 = 3x + 20 → x = 25. Therefore angle JHN = x + 20 = 45°.

Answer: 45°