Abcd Is Parallelogram In Which В€ Adc 75в° And Side Ab Is Produced To Point E As Shown In Figure

ABCD is a parallelogram in which ∠ADC = 75° and side AB is produced to point E as shown In the figure. Find x + y.

Answers:

Here, ∠C and ∠D are adjacent angles of the parallelogram
∴ ∠C + ∠D = 180°
⇒ x + 75° = 180°
⇒ x = 105°
Also, y = x = 105° [alt.int.angles]
Thus, x + y = 105° + 105° = 210°