Question

In a parallelogram ABCD, angle A: angle B =4:5, find the measures of the angle in the parallelogram.​

Answer 1

Answer:

let angleA and angleB be 4x and 5x respectively A/Q

=>angle A + angleB = 180°

=> 4x + 5x= 180°

=> 9x = 180°

=> x= 180°÷9

=>x= 20°

therefore

angleA = 4x= 4×20° = 80°

And

angleB = 5x = 5×20°= 100°

So,

angleA = angleC = 80°

And

angleB = angleD = 100°

Answer 2

Given,

In a parallelogram ABCD, angle A: angle B = 4:5.

To find,

The measures of the angles of the parallelogram.

Solution,

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

Let us assume that the measure of angle A is 4x° and the measure of angle B is 5x°, respectively.

{Since their ratio is equal to 4:5}

Geometrically,

The adjacent angles of a parallelogram are supplementary. Also, its opposite angles are equal.

{Statement-1}

Now, according to the question and statement-1;

The adjacent angles of a parallelogram are supplementary

=> In parallelogram ABCD, the adjacent angles, angle A and angle B are supplementary

=> (measure of angle A) + (measure of angle B) = 180°

=> 4x° + 5x° = 180°

=> 9x° = 180°

=> x = (180/9)

=> x = 20

So, the measure of angle A = 4x° = (4×20)° = 80°

The measure of angle B = 5x° = (5×20)° = 100°

{Equation-1}

Now, according to statement-1;

The opposite angles of the parallelogram are equal

=> Angle A = angle C

and, angle B = angle D

{Equation-2}

Combining equation-1 and equation-2, we get;

Angle A = angle C = 80°

Angle B = angle D = 100°

Hence, the angles of the parallelogram are 80°, 100°, 80°, and 100°, respectively.