Question

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

Answer 1

Let the angle be x
Its complement is 90-x
Its supplement is 180-x
According to the question,
90-x= (1/3) × (180-x)
3 (90-x) =180-x
270-3x=180-x
270-180=3x-x
2x=90
x=45
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Answer 2

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. 
$(90-x) * 3 = \frac{1}{3}(180-x) * 3$
$3(90-x) = 180-x$
$270 - 3x = 180 -x$
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°. 

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