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Question
A playground is in the form of a rectangle ATEF. Two players are standing at the points F and B where EF = EB. Find the values of x and y.
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Solution
Given, A rectangle ATEF in which EF = EB.
Then, ΔFEB is an isosceles triangle.
Therefore, by the angle sum property of a triangle, we have
∠EFB + ∠EBF + ∠FEB = 180° ...[Angle sum property of triangle]
⇒ ∠EFB + ∠EBF + 90° = 180° ...[∵ In a rectangle, each angle is of 90°]
⇒ 2∠EFB = 90° ...[∵ ∠EFB = ∠EBF]
∠EFB = 45° and ∠EBF = 45°
Now, ∠x = 180° – 45° = 135° ...[Linear pair]
And ∠EFB + ∠y = 90° ...[∵ In a rectangle, each angle is of 90°]
⇒ ∠y = 90° – 45° = 45°
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