In the following figure, the lines are parallel to each other as shown. Find the angles p, q, r and s.
A
p=110°,q=70°,r=70°,s=110°
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B
p=110°,q=70°,r=110°,s=110°
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C
p=70°,q=110°,r=70°,s=110°
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D
p=70°,q=70°,r=70°,s=110°
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Solution
The correct option is Dp=70°,q=70°,r=70°,s=110° From the figure, ∠1+110°=180° (Since co- interior angles are supplementary) ⇒∠1=180°−110° ⇒∠1=70° ... (i)
⇒p=70° ... (ii) (Since vertically opposite angles are equal)
⇒q=p=70° ... (iii) (Since corresponding angles are equal)
⇒s=110° ... (iv) (Since alternate interior angles are equal)
From (iii), r=q=70° ... (v) (Since alternate interior angles are equal)