Question

A triangle has two corners of angles `pi /8` and `(5pi)/6`. What are the complement and supplement of the third corner?

Answer 1

Complementary angle: `11/24pi`

Supplementary angle: `23/24pi`

Explanation:

Things to Remember
[1] The sum of the 3 interior angles of a triangle `=pi`
[2] Complementary angles add up to `pi/2`
[3] Supplementary angles add up to `pi`

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Given two angles `pi/8` and `(5pi)/6`
the third angle must be
`color(white)("XXX")=pi-(pi/8+(5pi)/6)`

`color(white)("XXX")=pi-((3pi+20pi)/24)`

`color(white)("XXX")=pi/24`

Complement of the third angle `=pi/2-pi/24= (11pi)/24`

Supplement of the third angle `=pi-pi/24=(23pi)/24`