Arun
Last Activity: 7 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 = 180y = 180. (3/5)y = 108Now put this value in equation (2) to get the value of x:x + 108 = 180x = 180 - 108x = 72Hence, the adjacent angles of a parallelogram are 72° and 108° .Hope it will help you.
Regards
Arun (askIITians forum expert)
