Question

A triangle has two corners of angles `pi /12` and `(5pi)/6`. What are the complement and supplement of the third corner?

Answer 1

`(5pi)/12" and " (11pi)/12`

Explanation:

The sum of the 3 angles in a triangle = `pi`

To find the size of the 3rd angle, subtract the sum of the 2 given angles from `pi`

That is `pi-(pi/12+(5pi)/6)`

`=pi-(pi/12+(10pi)/12)=pi-(11pi)/12=pi/12`

`color(blue)"Complementary angles are 2 angles whose sum is"pi/2`

The `color(blue)"complement"` to `pi/12` is therefore

`pi/2-pi/12=(6pi)/12-pi/12=color(blue)((5pi)/12)`

`color(red)"Supplementary angles are 2 angles whose sum is "pi`

The `color(red)"supplement"` to `pi/12` is therefore

`pi-pi/12=(12pi)/12-pi/12=color(red)((11pi)/12)`