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 . a Find the angles of △MNL.

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

(Please, make a drawing with the given information)

BL is an angular bisector for angle ABC.

LM is perpendicular to AB. Then, Angle BLM = 70 degrees( right angle, 20 degrees and 70 degrees.

The same observation for angle BLN will give that angle is 70 degree also.

We look at triangles BLM and BLN. They are congruent. They have a common side, BL and both have angles of 70 and 20 degrees. Therefore, BM is congruent to BN.

We look at triangle LMN. It is an isosceles triangle with vertex angle of 140 degrees.

We know, that the two base angles in isosceles triangle are congruent. This means, each of them is 20 degrees.