Question

In the given figure, $PQ||RT$. Find the value of $a+b$.

Answer 1

applying angle sum property in triangle PQR,

$\angle PRQ+\angle RQP+\angle QPR={180}^O$

$\angle PRQ+{45}^O+{55}^O={180}^O$

$\angle PRQ={80}^O$

$\angle PRQ+\angle QRT+\angle TRS={180}^O$ (angles forming a straight line)

${80}^o+a+b={180}^o$

$a+b={100}^o$