Question

A triangle has two corners of angles `(pi )/4` and `(5 pi)/12`. What are the complement and supplement of the third corner?

Answer 1

`pi/6" and " (2pi)/3`

Explanation:

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

hence 3rd angle`=pi-(pi/4+(5pi)/12)`

and`pi/4=pi/4xx3/3=(3pi)/12" equivalent fractions "`

`rArr"3rd angle "=pi-((3pi)/12+(5pi)/12)=pi-(8pi)/12`

and`(8pi)/12" simplifies to" (2pi)/3`

`rArr"3rd angle"=pi-(2pi)/3=(3pi)/3-(2pi)/3=pi/3`
`"-------------------------------------------------------------"`

2 angles are`color(blue)" complementary""when they add up to"pi/2`

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

2 angles are`color(red)"supplementary""when they add up to "pi`

`rArr"supplement of"pi/3=pi-pi/3=(3pi)/3-pi/3=(2pi)/3`