Question

in the adjoining figure ABCD is a trapezium in which a b is equal if angle equal to 55 degree and Angle B equal to 70 degree find angle C and angle d​

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 = 180°

To find ∠ D

∠ D = 180° – ∠ A

By substituting the value in the above equation

∠ D = 180° – 55°

By subtraction

∠ D = 125°

In a quadrilateral we know that the sum of all the angles is 360°

So we can write it as

∠ A + ∠ B + ∠ C + ∠ D = 360°

By substituting the values in the above equation

55° + 70° + ∠ C + 125° = 360°

On further calculation

∠ C = 360° – 55° – 70° – 125°

By subtraction

∠ C = 360° – 250°

∠ C = 110°

Therefore, ∠ C = 110° and ∠ D = 125°

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