if an angle of a parallelogram is two third of its adjacent angles find these two angles of parallelogram
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if an angle of a parallelogram is two third of its adjacent angles find these two angles of parallelogram
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Answer:
Let the adjacent angle be x °
then angle be 2x/3 °
[tex]x + \frac{2x}{3} = 180 \\ \frac{3x + 2x}{3} = 180 \\ \frac{5x}{3} = 180 \\ 5x = 180 \times 3 \\ x = \frac{540}{5} \\ x = 108 \\ [/tex]
angles are 108° and 72°
Answer:
Step-by-step explanation:
Given,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.
Given that one angle is two-third of its adjacent angle.
We assume that angle "x" is two-third of angle "y".
x = (2/3) y -- (1)
We know that the adjacent sides of a parallelogram are supplementary. It means that the sum of adjacent angles is equal to 180º.
So, x + y = 180º ------ (2)
Put the value of x from equation (1) in equation (2).
(2/3) y + y = 180 º
(2/3 +1) y = 180 º
(5/3) y = 180 º
y = 180º x (3/5)
y = 108º
Put this value in equation (2) to get the value of x-
x + 108º = 180º
x = 180º - 108 º
x = 72º
Hence, the adjacent angles of a parallelogram are 72° and 108° .