Question

In the given figure, ∠BAD = 78°, ∠DCF = x° and ∠DEF = y°. Find the values of x and y.

Answer 1

It is given that, and, are cyclic quadrilateral

We have to find the value of x and y.

Since , is a cyclic quadrilateral

So (Opposite angle of a cyclic quadrilateral are supplementary)

()

..… (1)

x = 180° − 102°
= 78°

Now in cyclic quadrilateral DCFE
x + y = 180° (Opposite angles of a cyclic quadrilateral are supplementary)
y = 180° − 78°
= 102°

Hence, x = 78° and y = 102°