InterviewSolution
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InterviewSolution
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In the adjoining figure, ABCD is a parallelogram in which ∠ DAB = 80° and ∠ DBC = 60°. Calculate ∠CDB and ∠ ADB. |
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Answer» It is given that ABCD is a parallelogram in which ∠ DAB = 80o and ∠ DBC = 60o We know that opposite angles are equal in parallelogram So we get ∠ C = ∠ A = 80o From the figure we know that AD || BC and BD is a transversal We know that ∠ ADB and ∠ DBC are alternate angles So we get ∠ ADB = ∠ DBC = 60o Consider △ ABD Using the sum property of triangle ∠ A + ∠ ADB + ∠ ABD = 180o By substituting values in the above equation 80o + 60o + ∠ ABD = 180o On further calculation ∠ ABD = 180o – 80o – 60o By subtraction ∠ ABD = 180o – 140o So we get ∠ ABD = 40o It can be written as ∠ ABC = ∠ ABD + ∠ DBC By substituting values we get ∠ ABC = 40o + 60o By addition ∠ ABC = 100o We know that the opposite angles are equal in a parallelogram ∠ ADC = ∠ ABC = 100o We get ∠ ADC = ∠ CDB + ∠ ADB On further calculation ∠ CDB = ∠ ADC – ∠ ADB By substituting values ∠ CDB = 100o – 60o By subtraction ∠ CDB = 40o Therefore, ∠ ADB = 60o and ∠ CDB = 40o. |
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