Answer :
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. Thanks.
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. Thanks.
Given-ABCD is a parallelogram
2/3of its adjencent angleis equal
To prove-All the andle of a parallelogram
Proof- we assume that X is2/3 of its angle Y
X=2/3y.......eqn1
It is also known that the adjacent side of a parallelogram are supplimentary.so the sum of adjencent angle is 180degree
X+Y=180degree......eqn2
put the value of X from equation 1in eqn2
2/3y+Y=180degree
(2/3+1)Y=180degree
( 5/3)y=180degree
Y=180*3/5
Y=540/5=180degree
now put this value in eqn2 to get value of X
X+108=180
X=72
Hence adjencent angle of the parallelogram are 72degree and 180 degree
2/3of its adjencent angleis equal
To prove-All the andle of a parallelogram
Proof- we assume that X is2/3 of its angle Y
X=2/3y.......eqn1
It is also known that the adjacent side of a parallelogram are supplimentary.so the sum of adjencent angle is 180degree
X+Y=180degree......eqn2
put the value of X from equation 1in eqn2
2/3y+Y=180degree
(2/3+1)Y=180degree
( 5/3)y=180degree
Y=180*3/5
Y=540/5=180degree
now put this value in eqn2 to get value of X
X+108=180
X=72
Hence adjencent angle of the parallelogram are 72degree and 180 degree