What are the values of x and y, if ABCD is a parallelogram?

As ABCD is a parallelogram, AB || CD

⇒ ∠CDB = ∠ABD and ∠CBD = ∠ADB  (Alternate interior angles of a parallelogram) 

Hence, 3y = 2x  ....(i)

And, x + y = 50^o   ....(ii)

Solving equations (i) and (ii), we get

3(50^o − x) = 2x

⇒ 150^o − 3x = 2x

⇒ 5x = 150^o

⇒ x = 30^o

From equation (ii),

30^o + y = 50^o

⇒ y = 50^o − 30^o

⇒ y = 20^o

Therefore, the values of x and y are 30^o and 20^o respectively.