Question

In a parallelogram, if one side is two-third of its adjacent side and the

perimeter of the parallelogram is 90cm, find the smallest side of the

parallelogram.​

Answer 1

Answer:Given that, if an angle of a parallelogram is two-third of its adjacent angle, we have to find the angles of the parallelogram.

Solution:

Let x and y be the two angles of a parallelogram.

It is given that one angle is two-third of its adjacent angle. So, we assume that angle "x" is two-third of angle "y" .

which is written as,

x = (2/3). y  ........ (1)

We also know that the adjacent sides of a parallelogram are supplementary. It means that the sum of adjacent angles is equal to 180.

Hence, x + y = 180   ........ (2)

Put the value of x from equation (1) in equation (2):

(2/3) y + y = 180

(2/3 +1) y = 180

(5/3) y = 180

y = 180. (3/5)

y =  108

Now put this value in equation (2) to get the value of x:

x + 108 = 180

x = 180 - 108

x = 72

Hence, the adjacent angles of a parallelogram are 72° and 108° .

Hope it will help you. Thanks

Step-by-step explanation:

Answer 2

Answer:

Let x and y be two adjacent angles of a parallelogram.

According to the question,

⇒ x= 2/3 y ----- ( 1 )

We know in parallelogram, sum of adjacent angles are supplementary.

∴ x+y=180°

=2/3y+y=180° [ From ( 1 ) ]

⇒ 5y=540°⇒ y=108°

Substituting value of y in equation ( 1 ) we get

≈ x=2/3×108°

≈ x= 72°

We know that, in parallelogram opposite angles are equal.

We know that, in parallelogram opposite angles are equal.∴ Four angles of parallelogram are 108° ,72°,108° and 72°