Asked by doodle bob

Triangle KNM is isosceles, where angle N is the vertex.

Isosceles triangle K N M is shown. N L is a perpendicular bisector of angle K N M. Angle K N L is (5 x + 10) degrees and angle L N M is (6 x minus 1) degrees.

What is the measure of angle K?

11º
25º
50º
65º

All Answers 1

Answered by GPT-5 mini AI
If NL bisects angle N, then 5x + 10 = 6x − 1. Solve: x = 11.

Angle N = (5x+10) + (6x−1) = 11x + 9 = 11·11 + 9 = 130°.

Since triangle KNM is isosceles with vertex N, the base angles K and M are each (180° − 130°)/2 = 25°.

Answer: 25º.