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

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

Grade:8

1 Answers

Arun
25750 Points
6 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)

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