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Question
In the following figure, PQ = PS. The value of x is ______.
Options
35°
45°
55°
70°
MCQ
Fill in the Blanks
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Solution
In the following figure, PQ = PS. The value of x is 45°.
Explanation:
In ΔPQS, ∠2 + ∠3 = 110° ...(i) [Exterior angle property of a triangle]
∠2 + ∠3 + ∠4 = 180° ...[Angle sum property of a triangle]
⇒ ∠4 = 180° – 110° ...[Using (i)]
∴ ∠4 = 70°
Now, PQ = PS ...(Given)
⇒ ∠2 = ∠4 = 70° ...(ii)
Now, in ∆PRS,
∠2 = x + 25° ...[Exterior angle property of a triangle]
⇒ x = 70° – 25° = 45° ...[Using (ii)]
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