Question

In the following figure, the lines are parallel to each other as shown. Find the angles p, q, r and s.

• A. $p=110°,q=70°,r=70°,s=110°$
• B. $p=110°,q=70°,r=110°,s=110°$
• C. $p=70°,q=110°,r=70°,s=110°$
• D. $p=70°,q=70°,r=70°,s=110°$

Answer 1

The correct option is D $p=70°,q=70°,r=70°,s=110°$


From the figure,
$\angle 1+110°=180°$
(Since co- interior angles are supplementary)
$\Rightarrow \angle 1=180°-110°$
$\Rightarrow \angle 1=70°$ ... (i)

$\Rightarrow p=70°$ ... (ii)
(Since vertically opposite angles are equal)

$\Rightarrow q=p=70°$ ... (iii)
(Since corresponding angles are equal)

$\Rightarrow s=110°$ ... (iv)
(Since alternate interior angles are equal)

From (iii), $r=q=70°$ ... (v)
(Since alternate interior angles are equal)

$\therefore p=70°,q=70°,r=70°,s=110°$