Question

Question #4c6e1

Answer 1

`\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!