Consider the required angle as x°
We know that the complement can be written as 90° – x° and the supplement can be written as 180° – x°
90° – x° = 1/3(180° – x°)
We can also write it as
90° – x° = 60° – (1/3) x°
So we get
x° – (1/3)x° = 90° – 60°
(2/3) x° = 30°
By division we get
x° = ((30×3)/2)
x° = 45°
Therefore, the angle whose complement is one third of its supplement is 45°.