In the given figure, ABCD is a parallelogram. What are the respective values of x° and y°?

ABCD is a parallelogram. So, its pairs of opposite sides are parallel.

∴AB||CD

Here, AC is transversal.

∴∠BAC = ∠ACD {Alternate angle}

⇒ ∠ACD = x°

⇒ x° = 66°

Or, ∠DCO = 66° ... (1)

Again, AB||CD and BD is a transversal line.

∴ ∠CDB = ∠ABD [Alternate angle]

∠CDB = 39°

Or, ∠CDO = 39° ... (2)

Now in ΔDOC,

∠CDO + ∠DCO + ∠COD = 180° [Angle sum property of triangle]

39° + 66° + y° = 180° [Using (1) and (2)]

⇒ y° = 180° − 105° = 75°

Thus, the respective values of x° and y° are 66° and 75°.