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sExercise 13.1If an angle of a parallelogram is two-thirds of its adjacent angle, farallelogram.driloteral are 1100 689 829 resnectively. Find t |
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Answer» Let x and y be the two angles of a parallelogram.It is given that one angle istwo-third of its adjacent angle. So, we assume that angle"x" is two-third of angle "y" .which can be 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° |
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