Question

$POQ$ is a straight line $OS$ bisects $\angle POR$. Show that $\angle SOT$ a right angle.

Answer 1

REF.Image

$\angle 1=\angle 2$ _______ (1)

$\angle 3=\angle 4$ _______ (2)

equation (1)+(2)

$\angle 1+\angle 3=\angle 2+\angle 4$ _______ (3)

$\angle 1+\angle 2+\angle 3+\angle 4=180$

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

$\angle 1+\angle 3=\frac{180}{2}={90}^{\circ }\Rightarrow \angle 2+\angle 3={90}^{\circ }$

$\angle 2+\angle 3=\angle SOT={90}^{\circ }$