Question

In the given figure, what is the value of 't' ? [2 marks]

Answer 1

The lines PQ, RS and UV intersect each other at the point O.
$\therefore \angle POR=\angle SOQ=2t°$
$\angle POU=\angle VOQ=5t°\left[\text{vertically opposite angles}\right]$ [1 Mark]

Also on the straight line RS, we have
$\angle ROV+\angle VOQ+\angle SOQ={180}^{\circ }\left[\text{Linear pair}\right]$
$\Rightarrow 5t°+5t°+2t°={180}^{\circ }$
$\Rightarrow 12t°={180}^{\circ }$
$\Rightarrow t°={15}^{\circ }$
$\Rightarrow t=15$ [1 Mark]