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Question
In the following figure, if QP || SR, the value of a is ______.
Options
40°
30°
90°
80°
MCQ
Fill in the Blanks
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Solution
In the following figure, if QP || SR, the value of a is 90°.
Explanation:
Draw a line LM passing through T such that LM || QP || SR.
Now, LM || QP and QT is a transversal.
∴ ∠PQT = ∠LTQ ...[Alternate interior angles]
⇒ 60° = ∠1 ...(i)
Also, LM || SR and TS is a transversal.
∴ ∠LTS = ∠TSR ...[Alternate interior angles]
⇒ ∠2 = 30° ...(ii)
From (i) and (ii), we get
a = ∠1 + ∠2 = 60° + 30° = 90°
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