Question

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

Answer 1

Step-by-step explanation:

Answer:

∠ C = 110 and ∠ D = 125

Given:

•ABCD is a trapezium

•AB || DC

•A = 55° and B = 70°

To Find:

•Angles of C and D=?

Solution:

We know that:

from 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

55 + 70 + ∠ C + 125 = 360

On further calculation

∠ C = 360o – 55o – 70o – 125o

By subtraction

∠ C = 360 – 250

∠ C = 110

Therefore, ∠ C = 110 and ∠ D = 125