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Question
In the following figure, if PQ || RS and QR || TS, then the value a is ______.
Options
95°
90°
85°
75°
MCQ
Fill in the Blanks
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Solution
In the following figure, if PQ || RS and QR || TS, then the value a is 95°.
Explanation:
Since, PQ || RS and RQ is a transversal
∴ ∠PQR = ∠QRS = 85° ...(i) [Alternate interior angles]
Also, RQ || TS and RS is a transversal.
∴ ∠QRS = ∠TSR = 85° ...(ii) [Using (i)] [Alternate interior angles]
Now, RS is a straight line.
∴ ∠RST + a = 180° ...[Linear pair]
⇒ 85° + a = 180° ...[Using (ii)]
⇒ a = 180° – 85° = 95°
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