Question

In the figure given, what is the value of $\angle t$?

• A. ${30}^{\circ }$
• B. ${40}^{\circ }$
• C. ${50}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is C

${50}^{\circ }$

In the given figure,
$\angle POR+\angle ROS+\angle SOQ={180}^{\circ }\left[\text{Angles on a straight line}\right]$
$\Rightarrow (t+{10}^{\circ })+t+(t+{20}^{\circ })={180}^{\circ }$

$\Rightarrow (3t+{30}^{\circ })={180}^{\circ }$

$\Rightarrow 3t={150}^{\circ }$

$\Rightarrow t={50}^{\circ }$