A triangle has two corners of angles π8 and π3. What are the complement and supplement of the third corner?

1 Answer
Nov 24, 2016

Complement: (π24) ... but see Note 1 below.

Supplement: 11π24

Explanation:

The complement of any angle θ is π2θ.

The supplement of any angle θ is πθ.

The Sum of the Interior Angles of a Triangle is π.

If two of the interior angles of a triangle are π8 and π3
then the third interior angle is π(π8+π3)=π11π24=13π24

The complement of this third angle is π213π24=π24
XXXNote 1: some people will claim that there is no
XXXcomplement for an angle which is greater than π2;
XXXcheck with your instructor.

The supplement of this third angle is π13π24=11π24.
XXXNote 2: the supplement of the third angle of a
XXXtriangle will always be the sum of the other two
XXXangles.