Question

If the angle of a parallelogram is two third its adjacent angles,find the angles of the parallelogram.​

Answer 1

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.

Step-by-step explanation:

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 know that the  the sum of adjacent angles is equal to 180

∴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:

108°, 72°

Step-by-step explanation:

let one angle be x,

then another adjacent angle = 2x/3

according to the property that in a parallelogram adjacent angles have sum 180°-

x+ 2x/3 = 180°

(3x+2x)/3 =180° ( because LCM of 1 and 3 is 3)

5x/3= 180°

5x = 180 × 3 ( transposing 3 to RHS)

5x= 540°

x= 540/ 5 ( transposing 5 to RHS)

x= 108°

First angle= x= 108°

Second angle = 2x/3= (2×108)/3= 216/3= 72°