Question

A triangle has two corners of angles `pi /6` and `(2pi)/3`. What are the complement and supplement of the third corner?

Answer 1

compemeent `=pi/3`
supplement `=(5pi)/6`

Explanation:

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

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

3rd angle `=pi-(pi/6+(2pi)/3)=pi-(pi/6+(4pi)/6)`

3rd angle `=pi-(5pi)/6=(6pi)/6-(5pi)/6=pi/6`
`"-----------------------------------------------------------"`
Complementary Angles are 2 angles whose sum is `pi/2`

To find the Complement of a given angle subtract it from `pi/2`

Complement of `pi/6=pi/2-pi/6=(3pi)/6-pi/6=(2pi)/6=pi/3`
`"--------------------------------------------------------------"`

Supplementary Angles are 2 angles whose sum is `pi`

To find the Supplement of a given angle subtract it from `pi`

Supplement of `pi/6=pi-pi/6=(6pi)/6-pi/6=(5pi)/6`