In the given figure, if QRS is an equilateral triangle and QTS is an isosceles triangle and x = 47, then the value (in degrees) of y will be

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Q: 132 (IAS/1997)
In the given figure, if QRS is an equilateral triangle and QTS is an isosceles triangle and x = 47°, then the value (in degrees) of y will be

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,1,6,1,0,5,1

keywords: 

{'equilateral triangle': [0, 1, 0, 1], 'isosceles triangle': [0, 1, 0, 0], 'qts': [0, 1, 0, 0], 'qrs': [0, 1, 0, 0], 'degrees': [0, 1, 0, 3], 'figure': [0, 1, 1, 0], 'value': [0, 0, 1, 0]}

In the mentioned problem, we are given that QRS is an equilateral triangle and QTS is an isosceles triangle.

In an equilateral triangle, all the angles are each 60°. As such, since we know that ∠QSR = 60°, and we are given that ∠TSQ = x = 47°, we can calculate ∠TSR (y) using the fact that the sum of the angles in a triangle is 180°.

Hence, ∠TSR (y) = 180 - 60 - 47 =73°.

However, for the isosceles triangle QTS, ∠QTS = ∠TQS because base angles in an isosceles triangle are equal. ∠QTS is made up of ∠QSR and ∠TSR which sums as 60° and 73° respectively giving 133°.

So, ∠TQS = 180 - 133 =47°. However, since we are given that x = ∠TQS = 47°, ∠TSQ should also equal 47°.

But that`s not possible as y = ∠TSR has been calculated as 73