Question

In the figure given, what is the value of 't' ?

• A. $5^{\circ }$
• B. ${10}^{\circ }$
• C. ${15}^{\circ }$
• D. ${20}^{\circ }$

Answer 1

The correct option is C ${15}^{\circ }$

The lines PQ, RS and UV intersect each other at the point O.
$\therefore \angle POU=\angle VOQ=5t°\left[\text{vertically opposite angles}\right]$

Also on the straight line RS, we have
$\angle ROV+\angle VOQ+\angle SOQ={180}^{\circ }\left[\text{angles on a straight line}\right]$
$\Rightarrow 5t+5t+2t={180}^{\circ }$
$\Rightarrow 12t={180}^{\circ }$
$\Rightarrow t={15}^{\circ }$