Question

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

In the figure, find the value of angles x and y.

Answer 1

We have to find the value of x and y.

Since ABCD is a cyclic quadrilateral.

∠A + angle BCD = 180° (Opposite angle of a cyclic quadrilateral are supplementary)

Step 1: 

∠BAD + ∠BCD = 180°

Given ∠BAD = 78°, we can find ∠BCD

78° + ∠BCD = 180°

∠BCD = 180° −  78°

∠BCD = 102°

Step 2: 

∠BCD + x = 180°

102° + x = 180°

x = 180° − 102°

x = 78°

Step 3: 

x + y = 180°

Substitute the value of x 

78° + y = 180°

y = 180° −  78°

y = 102°

The value of x is 78°, and the value of y is 102.