Question

Find an angle which is two-thirds of its COmplement

Answer 1

Let the angle be 'x'
And its complement angle be 'y'
By the problem,x=2/3y
We know that the sum of complementary angles is 90°
⇒y+2/3y=90°
⇒(3y+2y)/3=90°
⇒5y=270°
⇒y=54°
And x=2/3(54°)
⇒x=36°
Therefore the angles are 54°,36°.

Answer 2

sum of two complementary angles is 90.
let one of the angle be x.
a/q      2/3 of x +x= 90
            2x/3 +x=90
            (2x+3x)/3= 90
            5x= 90*3
             x= 270/5
          ∴x= 54
and 2/3 of 54= 2/3*54
                     = 2*18
                     = 36
 so one angle is 36 which is two third of its complement 54.they are complementary angles.
(36+54=90°)