Question:
In the given figure, ∠BAD = 75°, ∠DCF = x° and ∠DEF = y°. Find the values of x and y.
Solution:
We know that if one side of a cyclic quadrilateral is produced, then the exterior angle is equal to the interior opposite angle.
i.e., ∠BAD = ∠DCF = 75°
⇒ ∠DCF = x = 75°
Again, the sum of opposite angles in a cyclic quadrilateral is 180°.
Thus, ∠DCF + ∠DEF = 180°
⇒ 75° + y = 180°
⇒ y = (180° - 75°) = 105°
Hence, x = 75° and y = 105°