Question

in a trapezium ABCD, AB is parallel to CD and angle A measure 65 degrees find the measure of angle D?

a) 65
b) 115
c) 180​

Answer 1

Answer:

b)115

if the two lines are parallel and if any line intersects two lines in A and D then the angle A and angle D are supplementary to each other

angle D=180-angle A

=180-65

=115

Answer 2

Given,

In a trapezium ABCD, AB is parallel to CD.

The measure of angle A = 65°

To find,

The measure of angle D.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

In a trapezium, the two adjacent angles which have a common non-parallel side, are supplementary.

{Statement-1}

Now, according to the question and statement-1;

In trapezium ABCD, the non-parallel sides are AD and BC

=> Angle A + angle D = angle B + angle C = 180°

=> 65° + angle D = 180°

=> angle D = (180°-65°) = 115°

=> angle D = 115°

Hence, the measure of angle D is equal to 115°.