In an isosceles triangle ABC with base AC, angle B = 36 degrees, bisectors AD and CE meet at point O. Find angle EOA.

Since the triangle ABC is isosceles, the angle BAC = BCA = (180 – ABC) / 2 = (180 – 36) / 2 = 72.

Since AD and CE are bisectors, the angle ОАС = BAC / 2 = 72/2 = 36, the angle OCA = BCA / 2 = 72/2 = 36.

The sought angle EOA is the outer angle at the vertex O of the triangle AOC, which is equal to the sum of the inner angles that are not adjacent to it.

Angle EOA = OAC + OCA = 36 + 36 = 72.

Answer: Angle EOA is 72.