Question

In the adjoining figure, ABCD is a trapezium in which AB || DC. If ∠A = 55° and ∠B = 70°, find ∠C and ∠D.


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Answer 1

It is given that AB || DC From the figure we know that ∠ A and ∠ D are consecutive interior angles So it can written as

∠ A + ∠ D = 180⁰

To find ∠ D ∠ D = 180⁰– ∠ A

By substituting the value in the above equation

∠ D = 180⁰ – 55⁰

By subtraction ∠ D = 125⁰

In a quadrilateral we know that the sum of all the angles is 360o So we can write it as ∠ A + ∠ B + ∠ C + ∠ D = 360o⁰

By substituting the values in the above equation 55⁰ + 70⁰ + ∠ C + 125⁰= 360⁰

On further calculation ∠ C = 360⁰– 55⁰ – 70⁰ – 125⁰

By subtraction

∠ C = 360⁰ – 250⁰

∠ C = 110⁰

Therefore, ∠ C = 110⁰ and ∠ D = 125⁰

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Answer 2

Step-by-step explanation:

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