Question

A triangle has two corners of angles `pi /8` and `(7pi)/12`. What are the complement and supplement of the third corner?

Answer 1

`(5pi)/24" and " (17pi)/24`

Explanation:

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

To calculate the third angle, subtract the sum of the 2 given angles from `pi`

`"third angle " =pi-(pi/8+(7pi)/12)`

`=pi-((3pi)/24+(14pi)/24)=pi-(17pi)/24`

`=(24pi)/24-(17pi)/24=(7pi)/24larrcolor(red)"third angle"`

An angle and it's `color(blue)"complement"` sum to `pi/2`

`"complement of " (7pi)/24=(pi/2-(7pi)/24)`

`=(12pi)/24-(7pi)/24=(5pi)/24larrcolor(red)"complement"`

An angle and it's `color(blue)"supplement"` sum to `pi`

`"supplement of " (7pi)/24=(pi-(7pi)/24)`

`=(24pi)/24-(7pi)/24=(17pi)/24larrcolor(red)"supplement"`

`color(blue)"As a check"`

`(7pi)/24+(5pi)/24=(12pi)/24=pi/2color(white)(x)✔︎`

`"and " (7pi)/24+(17pi)/24=(24pi)/24=picolor(white)(xx)✔︎`