Question

if the complement of an angle is one - third of its supplement, find the angle

Answer 1

Let the angle be $x$°. 
Complement of x = (90-x)
Supplement of x = (180-x)

ATQ (According to question)
$(90-x) = \frac{1}{3}(180-x)$
Multiplying both sides by 3. 
$(90-x) * 3 = \frac{1}{3}(180-x) * 3$
$3(90-x) = 1(180-x)$
$270 - 3x = 180 - x$
Transposing -x to LHS and 270 to RHS. 
$-3x + x = 180 - 270$
$- 2x = -90$
Dividing both sides by -2. 
$\frac{-2x}{-2} = \frac{-90}{-2}$
$x = 45$

∴ The required angle is 45°. 

Hope this may help you.