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.

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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