A triangle has two corners of angles $\frac{π}{12}$ $pi /12$ and $\frac{7 π}{12}$ $(7pi)/12$ . What are the complement and supplement of the third corner?

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Answer 1 · 2017-11-09T17:39:43

The complement is $\frac{π}{6}$ $pi/6$ radians.

The supplement is $\frac{2 π}{3}$ $(2pi)/3$ radians.

First, we have to find the measure of the third corner.

The sum of the angles in any triangle is $180^{o}$ $180^o$ or $π$ $pi$ radians.
Therefore, $π - \frac{π}{12} - \frac{7 π}{12}$ $pi-pi/12-(7pi)/12$

$= π - \frac{8 π}{12}$ $=pi-(8pi)/12$

$= π - \frac{2 π}{3}$ $=pi-(2pi)/3$

$= \frac{3 π}{3} - \frac{2 π}{3}$ $=(3pi)/3-(2pi)/3$

$= \frac{π}{3}$ $=pi/3$

So the measure of the third angle is $\frac{π}{3}$ $pi/3$ .

Therefore, its complement is equal to:

$\frac{π}{2} - \frac{π}{3} = \frac{π}{6}$ $pi/2-pi/3=pi/6$ radians.

And its supplement is equal to:

$π - \frac{π}{3} = \frac{2 π}{3}$ $pi-pi/3=(2pi)/3$ radians.

A triangle has two corners of angles pi /12π12pi /12 and (7pi)/12 7π12(7pi)/12 . What are the complement and supplement of the third corner?