Question

The supplement of an angle is one - third of it. Determine the angle and it's supplement .
ANSWER= angle 135° and supplement = 45° but how????

Answer 1

let an angle be x.
then its supplement=180-x.

A/Q
SUPPLEMENT OF ANGLE =one third of the angle

180-x=x/3
3(180-x)=x.
540-3x=x
-3x-x=-540
-4x=-540
x=135degree

and its supplement=180-135=45degree

Answer 2

Let one angle be x degrees. Then its supplementary angle will be 180 - x degrees.
 
That means the two angles will be x and 180 - x.

Given that the supplementary of an angle is 1/3rd of it.

Hence the linear equation for the given statement is,

x = 1/3 * (180 - x)
 
   3x = 180 - x

   4x = 180

    x = 45.

Hence the required angles are x = 45 degrees and 180 - 45 = 135 degrees.


Hope this helps!