Question

join Q and S in the adjoining figure and prove that /_p + /_Q+
/_R+/_S = 360 degrees

Answer 1

$\textbf{ Hello Mate! }$

I am using "<" an angle for sake of covinience.

$\textbf{ Given }$ = PQRS is quadrilateral.

$\textbf{ To Prove }$ = <P + <Q + <R + <S = 360°

$\textbf{ To construct }$ = Join QS.

$\textbf{ Proof }$ = In triangle PQS :

<P + <PQS + < PSQ = 180° ( Angle sum pro. )

In triangle QRS :

<SQR + <R + <QSR = 180°

On adding both equation we get,

<P + ( <PQS + <SQR ) + <R + ( <PSQ + <QSR ) = 180° + 180°

<P + <Q + <R + <S = 360°

$\boxed{ Hence\:Proved }$

Have great future ahead!

Answer 2

This is your Answer...

Hope It Help You ☺️☺️