In triangle ABC AD is bisector, angle С = 104 degrees, angle CAD = 6. Find angle В

Given: triangle ABC; bisector AD; angle C = 104 °; angle CAD = 6 °.

Find: angle B.

Solution:

1) Since AD is a bisector, it divides angle A into two equal angles, hence the CAD angle is equal to the BAD angle.

2) Since we know the CAD angle, and the BAD angle is equal to it, we can find their sum making up the angle A: 6 + 6 = 12 °.

3) The sum of the angles in any triangle is 180 °, the angles A and C are known to us, so we can find the angle B: 180 – (104 + 12) = 64 °.

Answer: angle B = 64 °.