Question

15. In a cyclic quadrilateral ABCD, it is being given that
ZA = (x + y +10)°, ZB = (y +20)°, ZC = (x + y -30)°and ZD = (x+y) then ZB = ?​

Answer 1

In the given cyclic quadrilateral ABCD, the angles are given as follows :

Angle A = x + y + 10°

Angle B = y + 20°

Angle C = x + y - 30°

Angle D = x + y°

According to the properties of cyclic quadrilaterals , we know that opposite angles are supplementary or add upto 180°

Thus ,

Angle A + Angle C = 180°

Angle B + Angle D = 180°

This follows :

x + y + 10 + x + y - 30 = 180°

=> 2( x + y ) = 200°

=> x + y = 100°

y + 20 + x + y = 180°

=> x + 2y = 160°

=> ( x + y) + y = 160°

But x + y = 100°

So , y = 60°

Hence , x = 40°

Angle B = y + 20 = 80°

This is the required answer .

_____________________________________