Question

if the sum of two opposite angle of a parallelogram is 100° find the measure of each of its angles.​

Answer 1

Answer :-

Adjacent angle of parallelogram sums up to 180°.

Let the adjacent angle be x

x + 100° = 180°

x = 80°

Angles = 100° , 80° , 100° and 80°

Answer 2

Given:

The sum of two opposite angles of a parallelogram=100°

To find:

The measure of each of its angles

Solution:

The measure of each of its angles is 50°, 130°, 50°, and 130°.

We can find the measure by following the process given-

We know that the angles opposite to each other in a parallelogram are equal.

Similarly, the angles adjacent to each other in the parallelogram are supplementary.

Let the angles of the parallelogram are A, B, C, and D.

The opposite angles are A and C, B and D.

So, angle A=angle C and angle B=angle D.

We are given that the sum of the opposite angles is 100°.

Angle A+Angle C=100°

2(Angle A)=100°

Angle A=Angle C=50°

Now, the sum of any two adjacent angles is 180°.

So, angle A+angle B=180°

Substituting the value of angle A,

50°+angle B=180°

Angle B=180°-50°

Angle B=130°

Similarly, angle D=130°.

Therefore, the measure of each of its angles is 50°, 130°, 50°, and 130°.