Question

In the adjoining figure find the values of $x$ and $y$.

Answer 1

In the given figure

$\angle PQR+\angle SQP={180}^o$

$\angle =180-{115}^o={65}^o$ [liner pair]

now $\angle PQR=x=\angle PQR$ {given]

$\therefore \angle PQT=\angle PQR={65}^o$

Now In $\Delta PQR$

$\angle P+\angle Q+R={180}^o$ [ angle sum property]

$y+2x=180$

$y=180-130=50$

Hence $[x={65}^{o}andy={50}^o]$