Question

If QP || SR, the value of a is

• A. 40°
• B. 30°
• C. 90°
• D. 80°

Answer 1

The correct option is C 90°

Find the value of a
Given: QP || SR

Construction: Draw a line LM such that LM || QP || SR
As QP || LM
$\therefore \angle LTQ=\angle TQP$ (Alternate interior angles)
$\Rightarrow \angle LTQ={60}^{\circ }$
Also, LM || SR
$\therefore \angle LTS=\angle TSR$ (Alternate interiror angles)
$\Rightarrow \angle LTS={30}^{\circ }$
Thus, $a=\angle LTQ+\angle LTS$
$={60}^{\circ }+{30}^{\circ }$
$={90}^{\circ }$
Hence, (c) is the correct answer.