# If 3 times the supplement of an angle is subtracted from 7 times the complement of the angle, the answer is the same as that obtained from trisecting a right angle. What is the supplement of this angle?

Dec 5, 2015

${165}^{\circ}$

#### Explanation:

Let the unknown angle be $x$.

Hence the supplement of the angle is ${180}^{\circ} - x$.

The compliment of the angle is ${90}^{\circ} - x$.

Trisecting a right angle gives 3 angles of ${30}^{\circ}$.

Now writing an equation for the written information in the original question gives :

$7 \left(90 - x\right) - 3 \left(180 - x\right) = 30$

$\therefore 630 - 7 x - 540 + 3 x = 30$

$\therefore x = \frac{630 - 540 - 30}{7 - 3} = 15$

Therefore the supplement of the angle is $180 - 15 = {165}^{\circ}$.