Question

pqrs is a cyclic quadrilateral its diagnol pr and qs intersect each other at t if angle prs=80 and rqs=50 find angle psr

Answer 1

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Answer 2

The value of $\angle psr$ is $50\ degree$

Step-by-step explanation:

Given,

$pqrs$ is a cyclic quadrilateral its diagonal $pr$ and $qs$ intersect each other at $t$ if $\angle prs=80\ degree$ and $\angle rqs=50\ degree$

From figure,

$\angle pqs\ and\ \angle prs$

∴ $\angle pqs=\angle prs$ (∵ Angle made by same arc is equal)

∴ $\angle pqs=80\ degree$

∴ $\angle pqr=(80+50)=130\ degree$

Sum of opposite angle in cyclic quadrilateral is $180\ degree$)

∴ $\angle pqr+\angle psr=180\ degree$

⇒$\angle psr=(180-130)\ degree$

⇒$\angle psr=50\ degree$

So, The value of $\angle psr$ is $50\ degree$