Question

if an angle of a parallelogram is two third of its adjacent angles find these two angles of parallelogram​

Answer 1

Answer:

Let the adjacent angle be x °

then angle be 2x/3 °

$x + \frac{2x}{3} = 180 \\ \frac{3x + 2x}{3} = 180 \\ \frac{5x}{3} = 180 \\ 5x = 180 \times 3 \\ x = \frac{540}{5} \\ x = 108$

angles are 108° and 72°

Answer 2

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° .