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In the given figure , AC = BC. Find the value of x and y ?

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70 °, 125 °

80 °, 105 °

60 °, 125 °

80 °, 100 °

answer is A.

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Detailed Solution

In the given triangle ABC
We are given that AC = BC
This means that it is an isosceles triangle
And in an isosceles triangle the angles made by the equal sides are equal
⇒∠BAC=∠ABC
∠BAO=125

°

(Given)
⇒∠BAC+∠BAO=180

°

(angle formed by a straight line)
⇒∠BAC+125

°

=180

°

⇒∠BAC= 180

°

−125∘
⇒∠BAC= 55

°

Since, ∠BAC=∠ABC
We get ∠ABC=55

°

⇒∠ABC + y=180

°

(angle formed by a straight line)
⇒55

°

+y = 180

°

⇒y= 180

°

−55

°

⇒y= 125

°

⇒∠BAC+∠ABC+∠BCA=180

°

(angle sum property of triangle)
⇒55

°

+55

°

+x = 180

°

⇒110

°

+x = 180

°

⇒x = 180

°

−110

°

⇒x = 70

°

Hence we get the values of x and y to be 70

°

and 125

°

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