In the given figure, ABCD is a parallelogram. Side DC is produced to E and ∠BCE = 105°. Calculate ∠A, ∠B, ∠C and ∠D.

Given,

∠BCE = 105°

ABCD is a parallelogram.

⇒ ∠BCE + ∠BCD = 180° [Linear pairs]

⇒ ∠BCD = 180° - ∠BCE

⇒ ∠BCD = 180° - 105°

⇒ ∠BCD = 75°.

⇒ ∠A = ∠BCD = 75° [∵ opposite angles of a parallelogram are equal]

⇒ ∠A + ∠B = 180° [∵ AD ∥ BC and sum of Co-Interior angles is 180°]

⇒ ∠B = 180° - ∠A

⇒ ∠B = 180° - 75°

⇒ ∠B = 105°

⇒ ∠D = ∠B = 105° [∵ opposite angles of a parallelogram are equal]

Hence, ∠A = 75°, ∠C = 75°, ∠B = 105° and ∠D = 105°.