Question #4c6e1

1 Answer
Feb 22, 2018

#\text{Complementary Angle} = -\frac{\pi }{4}#

#\text{Supplementary Angle} = \frac{\pi }{4}#

Explanation:

A pair of angles whose sum is #pi/2# are known as complementary angles.

A pair of angles whose sum is #pi# are known as supplementary angles.

Let's say,

#x# be the complemetary angle of #{3pi}/4#, then by definition we will have:

#x=\pi/2-{3pi}/4#

#x=\frac{2\pi -3\pi }{4}#

Simplify to get:

#x=-\frac{\pi }{4}#

And, let's say the supplementary angle of the given angle is #y#, the according to the definition, the required angle is given by:

#y=\pi-{3pi}/4#

#=\frac{4\pi -3\pi }{4}#

Simplify:

#y=\frac{\pi }{4}#

That's it!