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?

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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?

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Answer 1 · 2016-01-31T03:32:09

$\frac{π}{12} rad$ $pi / 12 " rad"$

Explanation:

Let's try to write down what is being stated.

Let $θ$ $theta$ be the angle.
(7 times the complement of the angle) - (3 times the supplement of an angle) = one third of a right angle.
$\Rightarrow 7 (\frac{π}{2} - θ) - 3 (π - θ) = \frac{\frac{π}{2}}{3} = \frac{π}{6}$ $=> 7 ( pi / 2 - theta ) - 3 ( pi - theta ) = ( pi / 2 ) / 3 = pi / 6$
$\Rightarrow \frac{7 π}{2} - 7 θ - 3 π + 3 θ = \frac{π}{6}$ $=> ( 7 pi ) / 2 - 7 theta - 3 pi + 3 theta = pi / 6$
$\Rightarrow 4 θ = \frac{π}{2} - \frac{π}{6} = \frac{π}{3}$ $=> 4 theta = pi / 2 - pi / 6 = pi / 3$
$\Rightarrow θ = \frac{π}{12}$ $=> theta = pi / 12$ .

Remark :
Replace $π radians$ $pi " radians"$ by $180 degrees$ $180 " degrees"$ and continue the computation in the same way if you are more comfortable with degrees.

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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?

1 Answer

Explanation:

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