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(a) In the given figure, if $PQ \parallel RS$, then prove that $\Delta POQ \sim \Delta SOR$.
OR
(b) In the given figure, $\Delta OSR \sim \Delta OQP$, $\angle ROQ = 125^{\circ}$ and $\angle ORS = 70^{\circ}$. Find the measures of $\angle OSR$ and $\angle OQP$.
OR
(b) In the given figure, $\Delta OSR \sim \Delta OQP$, $\angle ROQ = 125^{\circ}$ and $\angle ORS = 70^{\circ}$. Find the measures of $\angle OSR$ and $\angle OQP$.
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Solution : (a) As $PQ \parallel RS$
$\angle P = \angle S$
$\angle Q = \angle R$ (Alternate interior angles)
$\therefore \Delta POQ \sim \Delta SOR$ (by AA similarity criterion)
OR
(b) $\angle OSR = 125^{\circ} - 70^{\circ} = 55^{\circ}$ [ by exterior angle property]
As $\Delta OSR \sim \Delta OQP$
$\angle OSR = \angle OQP$ (Corresponding angles of similar triangles)
$\angle OQP = 55^{\circ}$
$\angle P = \angle S$
$\angle Q = \angle R$ (Alternate interior angles)
$\therefore \Delta POQ \sim \Delta SOR$ (by AA similarity criterion)
OR
(b) $\angle OSR = 125^{\circ} - 70^{\circ} = 55^{\circ}$ [ by exterior angle property]
As $\Delta OSR \sim \Delta OQP$
$\angle OSR = \angle OQP$ (Corresponding angles of similar triangles)
$\angle OQP = 55^{\circ}$