A triangle has two corners of angles #pi /12# and #(3pi)/4 #. What are the complement and supplement of the third corner?

Question

A triangle has two corners of angles #pi /12# and #(3pi)/4  #.  What are the complement and supplement of the third corner?

Avery Allen · Accepted Answer

See explanation below

The sum of inner angles of a triangle is #pi# rads or #180# degrees The data are provided in rads. Lets operate Let #theta# the unknown angle in rads, then #theta+pi/12+3pi/4=pi# then #theta=pi-pi/12-3pi/4=pi/6# The complement will be #pi/6+alpha=pi/2# or #alpha=pi/2-pi/6=pi/3# The suplement will be #pi/6+beta=pi# or #beta=pi-pi/6=5pi/6#

Parker Allen · Answer

undefined The sum of the angles in a triangle is always $ \pi $ radians (180 degrees). So, to find the measure of the third angle, subtract the measures of the given angles from $ \pi $.

For the first angle, $ \frac{\pi}{12} $, and the second angle, $ \frac{3\pi}{4} $:

1. The measure of the third angle in radians is $ \pi - \frac{\pi}{12} - \frac{3\pi}{4} $.
2. Then, convert this result into degrees if necessary.

The complement of an angle is the difference between that angle and a right angle ($ \frac{\pi}{2} $ radians or 90 degrees). The supplement of an angle is the difference between that angle and a straight angle ($ \pi $ radians or 180 degrees).

So, to find the complement and supplement of the third angle:

1. For the complement, subtract the measure of the third angle from $ \frac{\pi}{2} $.
2. For the supplement, subtract the measure of the third angle from $ \pi $.