Question

in the adjoining figure PQRS is a cyclic quadrilateral .find angle X

Answer 1

Answer:

Sum of either pair of opposite angles of a cyclic quadrilateral is 180°.

Sum of angles of ∆PRS = 180°

angle S + angle R + angle P =

180°

Angle S + 35° + 50° = 180°

Angle S = 180° - 85°

Angle S = 95°

Angle S + Angle Q = 180°

Angle Q = 180°- 95°

Angle Q = 85°

Answer 2

Given:

An adjoining figure showing PQRS is a cyclic quadrilateral.

To find:

Angle x.

Solution:

As we know that in a cyclic quadrilateral ABCD having angle a, angle b, angle c and angle d, the sum of opposite angles is equal to 180° i.e. they are supplementary.

This means,

angle a + angle c = 180°

and

angle b + angle d = 180°

Also,

the sum of angles of a triangle is equal to 180°.

Now,

we have a cyclic quadrilateral PQRS where angle Q = x degree

And

angle S + angle Q = 180° ... (i)

Now,

In a triangle PRS,

50° + 35° + angle S = 180°

85° + angle S = 180°

angle S = 180° - 85°

So,

angle S = 95°

On putting the value of angle S in (i), we get

95° + angle Q = 180°

angle Q = 180° - 95°

angle Q = 85° = x

Hence, the value of x is 85°.