A triangle has two corners of angles #pi /8# and #(pi)/6 #. What are the complement and supplement of the third corner?

Question

A triangle has two corners of angles #pi /8# and #(pi)/6  #.  What are the complement and supplement of the third corner?

Claire Akin · Accepted Answer

supplement #(7pi)/24#. There is no complement.

The third orner of the triangle would be #pi-pi/8-pi/6=(17pi)/24#. Its supplement would be #pi-(17pi)/24= (7pi)/24# There would be no complement

Parker Allen · Answer

undefined The sum of the angles in a triangle is always $ \pi $ radians (180 degrees). Given that two angles of the triangle are $ \frac{\pi}{8} $ and $ \frac{\pi}{6} $, we can find the measure of the third angle by subtracting the sum of the known angles from $ \pi $:

$ \text{Third angle} = \pi - \left( \frac{\pi}{8} + \frac{\pi}{6} \right) $

$ = \pi - \frac{7\pi}{24} - \frac{4\pi}{24} $

$ = \pi - \frac{11\pi}{24} $

$ = \frac{13\pi}{24} $

The complement of an angle is the angle that, when added to it, results in a right angle, which is $ \frac{\pi}{2} $ radians (90 degrees). Thus, the complement of the third angle is:

$ \text{Complement} = \frac{\pi}{2} - \frac{13\pi}{24} $

$ = \frac{12\pi}{24} - \frac{13\pi}{24} $

$ = -\frac{\pi}{24} $

The supplement of an angle is the angle that, when added to it, results in a straight angle, which is $ \pi $ radians (180 degrees). Therefore, the supplement of the third angle is:

$ \text{Supplement} = \pi - \frac{13\pi}{24} $

$ = \frac{24\pi}{24} - \frac{13\pi}{24} $

$ = \frac{11\pi}{24} $