The bisectors AK, BL and CM are drawn in this triangle ABC. It is given that the angle KAC = 30

The bisectors AK, BL and CM are drawn in this triangle ABC. It is given that the angle KAC = 30 degrees and the angle MCA = 20 degrees. Find Angle B

It is known:

Triangle ABC.
AK, BL and CM are bisectors.
KAC angle = 30 °;
Angle MCA = 20 °.
Find angle B.

1) KAС angle = KAB angle;

This means that the angle CAB = angle KAC + angle KAВ = 30 ° + 30 ° = 60 °;

2) Since angle ACM = angle of MCB, then:

ACB angle = ACM angle + MCB angle = 20 ° + 20 ° = 40 °;

3) The sum of the angles of the triangle ABC = 180 °.

Then we find the angle B.

Angle B = 180 ° – Angle A – Angle B = 180 ° – 60 ° – 40 ° = 120 ° – 40 ° = 80 °.

From this we get that the angle B of the triangle ABC is equal to 80 °.

Answer: angle B = 80 °.