Question

In the figure ,PQRS is a cyclic quadrilateral. find the value of x.​

Answer 1

Answer:

Step-by-step explanation:

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

AnsWeR :

$\large \implies \angle Q (x) = 85\degree$

Solution :

From triangle SPR :

We know that,

Some of all angles of a triangle = 180°

so,

$\sf \angle S + \angle P+ \angle R = 180\degree$

➩ $\sf \angle S + 35 + 50 = 180\degree$

➩ $\sf \angle S + 85 = 180\degree$

➩ $\sf \angle S = 180\degree - 85$

➩ $\sf \boxed{\angle S = 95 \degree}$

Now,

PQRS is a cyclic quadrilateral.

Sum of the opposite angles of a cyclic quadrilateral = 180°

So,

$\angle S + \angle Q = 180 \degree \\ \\ \implies 95\degree + x = 180 \degree \\ \\ \implies x = 85 \degree$

Therefore,

value of x = 85°