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Question

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 D p=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)

p=70°,q=70°,r=70°,s=110°

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