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

$5^{\circ}$

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$10^{\circ}$

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$15^{\circ}$

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$20^{\circ}$

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Solution

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

The lines PQ, RS and UV intersect each other at the point O.
$∴ ∠ P O U = ∠ V O Q [vertically opposite angles]$

Also on the straight line RS, we have
$∠ R O V + ∠ V O Q + ∠ S O Q = 180^{\circ} [angles on a straight line]$
$\Rightarrow 5 t + 5 t + 2 t = 180^{\circ}$
$\Rightarrow 12 t = 180^{\circ}$
$\Rightarrow t = 15^{\circ}$

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