Question

Triangle L N M is cut by a bisector that forms a right angle with the base and splits the base into 2 congruent lengths. The lengths of sides L N and N M are congruent. Angle L N M is (6 x + 1) degrees. Angle N M L is (4 x minus 11) degrees.
What is the measure of ∠NLM?

m∠NLM =

Answer 1

LN = NM so triangle is isosceles with base LM. Thus the base angles are equal:
∠NLM = ∠NML = 4x − 11.

Sum of angles:
(6x + 1) + 2(4x − 11) = 180
6x + 1 + 8x − 22 = 180
14x − 21 = 180
14x = 201
x = 201/14.

So
m∠NLM = 4x − 11 = 4(201/14) − 11 = 325/7 ≈ 46.4286°.

Answer: 325/7 degrees (about 46.43°).