Question

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

Answer 1

Answer:

$\huge\underline\mathfrak\pink{♡AnSwEr♡}$

In ∆PSR,

∠SPR+∠SRP+∠PSR=180⁰ (Angle sum property of∆)

=>35⁰+50⁰+∠PSR=180⁰

=>∠PSR=(180⁰-85⁰)

=>∠PSR=95⁰------(i)

Since, Quadrilateral PQRS lie on circle.

Therefore it is cyclic.

And as we know sum of opposite angle of of a cyclic quadrilateral is 180⁰

So,

∠PSR+∠PQR=180⁰

=>95⁰+∠PQR=180⁰

=>∠PQR=85⁰

=>x=85⁰

There's your answer ✌️

Answer 2

Answer:

$\huge{ \mathtt{ \blue{ \underline{ \underline{Required \: answer \: }}}}}$

Solution:

⇨★ In ∆PRS, by using angle sum property, we have

∠PSR + ∠SRP + ∠RPS = 180°

∠PSR + 50° + 35o = 180°

∠PSR = 180° – 85o = 95°

Since PQRS is a cyclic quadrilateral

∴ ∠PSR + ∠PQR = 180°

[∵ opp. ∠s of a cyclic quad. are supplementary]

95° + x = 180°

x = 180° – 95°

x = 85°

Therefore, 85°

$\huge\boxed{\fcolorbox{blue}{orange}{hope it helps}}$