A triangle has two corners of angles $\frac{π}{8}$ $pi /8$ and $\frac{π}{3}$ $(pi)/3$ . What are the complement and supplement of the third corner?

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A triangle has two corners of angles $\frac{π}{8}$ $pi /8$ and $\frac{π}{3}$ $(pi)/3$ . What are the complement and supplement of the third corner?

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Answer 1 · 2016-11-24T14:41:50

Complement: $(- \frac{π}{24})$ $(-pi/24)$ ... but see Note 1 below.

Supplement: $\frac{11 π}{24}$ $(11pi)/24$

Explanation:

The complement of any angle $θ$ $theta$ is $\frac{π}{2} - θ$ $pi/2-theta$ .

The supplement of any angle $θ$ $theta$ is $π - θ$ $pi-theta$ .

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

If two of the interior angles of a triangle are $\frac{π}{8}$ $pi/8$ and $\frac{π}{3}$ $pi/3$
then the third interior angle is $π - (\frac{π}{8} + \frac{π}{3}) = π - \frac{11 π}{24} = \frac{13 π}{24}$ $pi-(pi/8+pi/3)=pi-(11pi)/24= (13pi)/24$

The complement of this third angle is $\frac{π}{2} - \frac{13 π}{24} = - \frac{π}{24}$ $pi/2-(13pi)/24=-pi/24$
$XXX$ $color(white)("XXX")$ Note 1: some people will claim that there is no
$XXX$ $color(white)("XXX")$ complement for an angle which is greater than $\frac{π}{2}$ $pi/2$ ;
$XXX$ $color(white)("XXX")$ check with your instructor.

The supplement of this third angle is $π - \frac{13 π}{24} = \frac{11 π}{24}$ $pi-(13pi)/24=(11pi)/24$ .
$XXX$ $color(white)("XXX")$ Note 2: the supplement of the third angle of a
$XXX$ $color(white)("XXX")$ triangle will always be the sum of the other two
$XXX$ $color(white)("XXX")$ angles.

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A triangle has two corners of angles $\frac{π}{8}$ $pi /8$ and $\frac{π}{3}$ $(pi)/3$ . What are the complement and supplement of the third corner?

1 Answer

Explanation:

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A triangle has two corners of angles $\frac{π}{8}$ $pi /8$ and $\frac{π}{3}$ $(pi)/3$ . What are the complement and supplement of the third corner?