Question

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

Answer 1

`(11pi)/24" and "(23pi)/24`

Explanation:

`"the third angle of the triangle is"`

`pi-(pi/12+(7pi)/8)=pi-(23pi)/24=pi/24`

`• " complementary angles sum to "pi/2`

`"complement of "pi/24=pi/2-pi/24=(12pi)/24-pi/24=(11pi)/24`

`• " supplementary angles sum to "pi`

`"supplement of "pi/24=pi-pi/24=(23pi)/24`

Answer 2

Complementary angle is `(11pi)/24`

Supplementary angle is `(23pi)/24`

Explanation:

All angles sum to `pi`

Third angle is:

`pi-(pi/12+(7pi)/8)`

`pi-(23pi)/24=pi/24`

An angle and its complement add up to `pi/2`

`(pi)/24+theta=pi/2=>theta=(11pi)/24`

An angle and its supplement add up to `pi`

`pi/24+theta=pi=>theta=pi-pi/24=(23pi)/24`

`:.`

Complementary angle is `(11pi)/24`

Supplementary angle is `(23pi)/24`