ABCD is a cyclic trapezium whose sides AD and BC are parallel to each other; if ∠ABC = 75° then the measure of ∠BCD is:

A. 75°

B. 95°

C. 45°

D. 105°

Answer: Option A

Solution(By Examveda Team)

According to figure
⇒ AD || BC
⇒ ∠ABC = 75°
Then
⇒ ∠ABC + ∠ADC = 180°
⇒ 75° + ∠ADC = 180°
⇒ ∠ADC = 180° - 75°
⇒ ∠ADC = 105°
⇒ As we know in a cyclic trapezium
∠ADC + ∠DCB = 180°
(AD || BC, corresponding angle)
⇒ 105° + ∠DCB = 180°
⇒ ∠DCB = 75°