Question

In the given figure $AS\parallel BT$; $\angle 4=\angle 5$
$\overline{SB}$ bisects $\angle AST$.find the measure of $\angle 1$

• A. $\angle 1={80}^{\circ }$
• B. $\angle 1={60}^{\circ }$
• C. $\angle 1={70}^{\circ }$
• D. $\angle 1={20}^{\circ }$

Answer 1

The correct option is B $\angle 1={60}^{\circ }$

Given, $\angle 4=\angle 5$ $⟹\angle 3=\angle 4=\angle 5={60}^{\circ }$ --- if 2 angles are equal, then they are equal to third.

Given, $SB$ is the bisector of $\angle AST$

$\Rightarrow \angle BST=\angle ASB={60}^{\circ }$

$\angle RST=\angle RSA+\angle ASB+\angle BST={180}^{\circ }$ --- angles on a straight line

$\Rightarrow \angle RSA={180}^{\circ }-{60}^{\circ }-{60}^{\circ }={60}^{\circ }$

$\therefore \angle 1={60}^{\circ }$