Question

In the adjoining figure, ABCD is a trapezium in which AB || DC. IF ∠A = 35° and ∠B = 75°, then find ∠C and ∠D.​

Answer 1

Answer:

∠ A + ∠ D = 180o To find ∠ D ∠ D = 180o – ∠

∠ D = 180o – 55o By subtraction ∠ D = 125

So we can write it as ∠ A + ∠ B + ∠ C + ∠ D = 360o .

55o + 70o + ∠ C + 125o = 360o On further calculation ∠ C = 360o – 55o – 70o – 125o By subtraction ∠ C = 360o – 250o ∠ C = 110o

Step-by-step explanation:

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 = 180o.

To find ∠ D ∠ D = 180o – ∠ A By substituting the value in the above equation

∠ D = 180o – 55o

By subtraction ∠ D = 125o

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

So we can write it as ∠ A + ∠ B + ∠ C + ∠ D = 360o

By substituting the values in the above equation 55o + 70o + ∠ C + 125o = 360o

On further calculation

∠ C = 360o – 55o – 70o – 125o

By subtraction ∠ C = 360o – 250o ∠ C = 110o Therefore, ∠ C = 110o and ∠ D = 125o.