Question

In the given figure, ∠BAD = 75°, ∠DCF = x° and ∠DEF = y°. Find the values of x and y.

Answer 1

In a cyclic quadrilateral we know that the exterior angle is equal to the interior opposite angle

So we get

∠BAD = ∠DCF = 75^o

It can be written as

∠DCF = x = 75^o

We get x = 75^o

We know that the opposite angles of a cyclic quadrilateral is 180^o

So we get

∠DCF + ∠DEF = 180^o

By substituting the values

75^o + ∠DEF = 180^o

On further calculation

∠DEF = 180^o – 75^o

By subtraction

∠DEF = y = 105^o

Therefore, the values of x and y is 75^o and 105^o.