In the diagram, PQR is a straight line, QRST is a parallelogram$\angle TPQ={{72}^{\circ }}$ and $\angle RST={{126}^{\circ }}$. What type of triangle is ΔPQT
An equilateral triangle
A right angled triangle
An Isosceles triangle
A scalene triangle
$\begin{align} & \angle TQR=\angle TSR={{126}^{\circ }}\text{ }\!\!\{\!\!\text{ opposite }\angle s\text{ of a }\text{ are equal}\} \\ & \angle TQP={{180}^{\circ }}-\angle TQR={{180}^{\circ }}-{{126}^{\circ }}={{54}^{\circ }}\text{ }\!\!\{\!\!\text{ sum of }\angle s\text{ a straight line }\!\!\}\!\!\text{ } \\ & \vartriangle TPQ \\ & \angle PTQ={{180}^{\circ }}-(\angle TQP+\angle TPQ)={{180}^{\circ }}-({{72}^{\circ }}+{{54}^{\circ }})={{54}^{\circ }} \\ & \vartriangle PQT\text{ is an isosceles triangle}\text{.} \\\end{align}$