InterviewSolution
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InterviewSolution
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In the figure given below, ABCD is a rectangle. Find the values of x and y. |
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Answer» From the figure we know that the diagonals of a rectangle are equal and bisect each other. Consider △ AOB We get OA = OB We know that the base angles are equal ∠ OAB = ∠ OBA By using the sum property of triangle ∠ AOB + ∠ OAB + ∠ OBA = 180o By substituting the values 110o + ∠ OAB + ∠ OBA = 180o We know that ∠ OAB = ∠ OBA So we get 2 ∠ OAB = 180o – 110o By subtraction 2 ∠ OAB = 70o By division ∠ OAB = 35o We know that AB || CD and AC is a transversal From the figure we know that ∠ DCA and ∠ CAB are alternate angles ∠ DCA = ∠ CAB = yo = 35o Consider △ ABC We know that ∠ ACB + ∠ CAB = 90o So we get ∠ ACB = 90o – ∠ CAB By substituting the values in above equation ∠ ACB = 90o – 35o By subtraction ∠ ACB = x = 55o Therefore, x = 55o and y = 35o. |
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