Question

In △ABC, m∠ABC=40°, BL (L∈ AC ) is the angle bisector of ∠B. Point M∈ AB so that LM ⊥ AB and N∈ BC so that LN ⊥ BC. Find the angles of △MNL.

Answer 1

20° 20° 140°

Explanation:

Answer 2

A diagram helps.

∆BNL and ∆BML are congruent right triangles (given one angle and congruent hypotenuse BL). So, ∆MNL is isosceles, with angle L being 180° - 40° = 140°

Then angles M and N of that triangle are each 20°.

The angles M, N, L of ∆MNL are 20°, 20°, 140°.