In an isosceles triangle ABC with base AC, angle B = 40º, AK is the bisector of angle A. Find the value of the angle KAC.

In an isosceles triangle, the angles at the base are equal to each other. The angles of a triangle add up to 180 °. Find the angle A at the base of the AC:

∠А = (180 ° – ∠В) / 2 = (180 ° – 40º) / 2 = 140º / 2 = 70º.

Since AK is the bisector of angle A, then ∠KAС is equal to half of angle A:

∠KAС = ∠A / 2 = 70º / 2 = 35º.

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