Question

find largest angle of a parallelogram if one angle of the parallelogram is 4 less than one-third of its adjacent angle

Answer 1

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° .

Answer 2

Answer:

44

Step-by-step explanation:

x+1/3x_4=180

(adjacent angles sum upto 180)

x+1/3x=176

4x=176

x=44

hence , the largest angle is 44