In figure (2) given below, ABCD is a parallelogram. Find the angles of △AOD.

Sum of angles of a triangle = 180°

In △BOC,

⇒ ∠BOC + ∠OCB + ∠CBO = 180°

⇒ ∠BOC + 35° + 77° = 180°

⇒ ∠BOC = 180° - 35° - 77° = 68°.

From figure,

∠AOD = ∠BOC = 68° (Vertically opposite angles are equal)

∠OAD = ∠OCB = 35° (Alternate angles are equal)

∠ADO = ∠CBO = 77° (Alternate angles are equal)

Hence, ∠AOD = 68°, ∠OAD = 35°, ∠ADO = 77°.