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

Since LN = NM, the base angles at L and M are equal, so ∠NLM = ∠NML = 4x − 11.

Sum of triangle angles:
(6x + 1) + (4x − 11) + (4x − 11) = 180
14x − 21 = 180
14x = 201
x = 201/14

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

So m∠NLM = 325/7 degrees (about 46.43°).