In the given figure, two straight lines AB and CD intersect at a point O. If ∠BOD = 40°, find the measure of each of the angles, ∠BOC, ∠AOC and ∠AOD.

Given:

∠BOD = 40°

When two lines intersect, the angles opposite to each other are equal.

∠AOC = ∠BOD $\quad$ [Vertically opposite angles]

∴ ∠AOC = 40°

Since AOB is a straight line, ∠BOC and ∠BOD form a linear pair and must sum to 180°

∠BOC + ∠BOD = 180°

Substituting the value of ∠BOD in above, we get:

⇒ ∠BOC + 40° = 180°

⇒ ∠BOC = 180° - 40°

⇒ ∠BOC = 140°

∠AOD = ∠BOC $\quad$ [Vertically opposite angles]

∴ ∠AOD = 140°

∠AOC = 40°, ∠BOC = 140° and ∠AOD = 140°.