In △ABC, AB = AC, O is a point on BC such that BO = CO and OD is perpendicular to AB and OE is perpendicular to AC. If ∠BOD = 60°, then measure of ∠AOE is:

30°

△OBD is a right-angled triangle at D and ∠BOD = 60°

So, ∠OBD = 90° - 60° = 30°

Since in △ABC, AB = AC, ∠OBD = ∠ACB = ∠ABC = 30°

So, ∠BAC = 180° - 2 x 30° = 120°

Since BO = OC, AO is a median.

According to the concept,

∠BAO = ∠OAC =∠OAE = \(\frac{120}{2}\) = 60°

Since OE is perpendicular to AC, △OEA is a right-angled triangle at E.

∠AOE = 90° - 60° = 30°

Therefore, ∠AOE = 30°.