# In triangle ABC, bisector AK is drawn, find angle B if angle C = 30 degrees, and angle AKC = 110 degrees

June 26, 2021 | education

| Consider the triangle AKS and find the angle CAK in it, knowing the other two angles.

∠САK = 180 ° – (∠ С + ∠ АКС) = 180 ° – (30 ° + 110 °) 180 ° – 140 ° = 40 °.

We find the angle A of the triangle ABC:

∠ А = 2 * ∠САK = 80 ° (AK – bisector by condition).

Two angles of the triangle ABC are known, we find the angle B:

∠ B = 180 ° – (∠ A + ∠ C) = 180 ° – (80 ° + 30 °) = 70 °.

Answer: The degree measure of angle B is 70 °.

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