Question

In the given figure, $\angle BAD={75}^{\circ },\angle DCF=x^{\circ }and\angle DEF=y^{\circ }$. Find the values of x and y.

Answer 1

ANSWER:
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°