Question

The supplement of the complement of an angle less the complement of an angle exceeds the quotient of the supplement of the angle and the number 3 by 73. Find the angle.

Answer 1

Complement of an angle = 90° - x.

Supplement of the complement of an angle = 180 - (90 - x).

= 180 - 90 + x

= 90 + x

Supplement of the complement of an angle less the complement of an angle = (90 + x) - (90 - x)

= 90 + x - 90 + x

= 2x

Now, the quotient of the supplement of the angle and the number 3 is $\frac{180-x}{3}$.

It is given that supplement of the complement of an angle less the complement of an angle exceeds the quotient of the supplement of the angle and the number 3 by 73.

Therefore, 2x = $\frac{180x}{3} +73$

$2x=\frac{180-x+219}{3}$

Multiply both sides by 3.

6x = 180 - x + 219

= 399 - x

Add x to both sides.

6x + x = 399

7x = 399

Divide both sides by 7.

x = 57

Hence, the required angle = 57°.