Find the measure of $∠ P$ and $∠ S$ if SP || RQ. (If you find m $∠ R$ , is there more than one method to find m $∠ P$ ) ?

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Solution

$H e r e, ∠ P + ∠ Q = 180^{\circ} [S u m o f c o - i n t e r i o r a n g l e s i s 180^{\circ}] \Rightarrow ∠ P + 130^{\circ} = 180^{\circ} \Rightarrow ∠ P = 180^{\circ} - 130^{\circ} \Rightarrow ∠ P = 50^{\circ} ∠ R = 90^{\circ} [G i v e n] ∠ S + 90^{\circ} = 180^{\circ} [S u m o f c o - i n t e r i o r a n g l e s i s 180^{\circ}] \Rightarrow ∠ S = 180^{\circ} - 90^{\circ} \Rightarrow ∠ S = 90^{\circ}$

$Y e s, w e c a n u s e a n o t h e r m e t h o d t o f i n d ∠ P ∠ S + ∠ R + ∠ Q + ∠ P = 360^{\circ} [A n g l e s u m p r o p e r t y o f q u a d r i l a t e r a l] \Rightarrow 90^{\circ} + 90^{\circ} + 130^{\circ} + ∠ P = 360^{\circ} \Rightarrow 310^{\circ} + ∠ P = 360^{\circ} \Rightarrow ∠ P = 360^{\circ} - 310^{\circ} \Rightarrow ∠ P = 50^{\circ}$

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