Question

In given figure, PQRS is a parallelogram RT and QT are bisectors of $\angle R$ and $\angle Q$ respectively meeting at T. find the measure of $\angle T$

Answer 1

In parallelogram $\angle R+\angle Q={180}^{\circ }$ (sum of adjacent angles in a parallelogram is ${180}^{\circ }$ -----(1)

$\angle 1=\angle 2$ and $\angle 3=\angle 4$ [RT and QT are angle bisectors]

From (1)

$\angle 1+\angle 2+\angle 3+\angle 4={180}^{\circ }$

$⟹2\angle 1+2\angle 3={180}^{\circ }$

$\therefore \angle 1+\angle 3={90}^{\circ }$

$\therefore \angle T=180-{90}^{\circ }={90}^{\circ }$ [sum of angles in a triangle $={180}^{\circ }$ ]