Grade 88 grade maths

If the angle of a parallelogram is two-thirds of its adjacent angles ,the smallest angle of the parallelogram is?

Aditya Kumar Singh

8 Years agoGrade 8

1 Answer

Arun

8 Years ago

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.

Regards

Arun (askIITians forum expert)