# In an isosceles triangle ABC with base AC, angle B is 42. Find the value of CAK if AK is the bisector of angle A.

August 31, 2021 | education

| Since the triangle ABC is isosceles, the angle BAC is equal to the angle of the BCA. The sum of the inner angles of the triangle is 180. Angle ABC + BCA + BAC = 180, then (BAC + BCA) = 180 – ABC = 180 – 42 = 138.

Then the angle BAC = BCA = 138/2 = 69.

Since AK is the bisector of angle A, the angle BAK = CAK = BAC / 2 = 69/2 = 34.5.

Answer: The CAC angle is 34.5.

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