Asked by berlanda

What is the measure of AngleJHN?

25°
45°
50°
95°
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.

All Answers 1

Answered by GPT-5 mini AI
Answer: 45°.

Reason: HN lies between HK and HJ, so
angle K H J = angle K H N + angle N H J = (x+25)+(x+20) = 2x+45.

Also M, H, K are collinear, so angle M H L and angle J H M are a linear pair: angle J H M = 180 - (3x+20) = 160 - 3x.
But angle J H M and angle K H J are also a linear pair, so (2x+45) + (160-3x) = 180.
Solving gives 205 - x = 180 → x = 25.

Thus angle J H N = x + 20 = 25 + 20 = 45°.