A triangle has two corners of angles $\frac{π}{8}$ $pi /8$ and $\frac{5 π}{8}$ $(5pi)/8$ . 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 $\frac{5 π}{8}$ $(5pi)/8$ . What are the complement and supplement of the third corner?

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Answer 1 · 2017-01-13T04:10:04

I'm assuming you want answers in radians, so here they are:
Complement = $\frac{π}{4}$ $pi/4$ radians
Supplement = $\frac{3 π}{4}$ $(3pi)/4$ radians

Explanation:

Since we are working with a denominator of 8, let's convert our basic radian measures to a denominator of 8 to make this more easy to work with.

90 degrees = $\frac{4 π}{8}$ $(4pi)/8$ radians
180 degrees = $\frac{8 π}{8}$ $(8pi)/8$ radians

The supplement is quite easy to find:

All 3 angles of a triangle add up to 180 degrees ( $\frac{8 π}{8}$ $(8pi)/8$ radians)
Supplementary angles add up to 180 degrees ( $\frac{8 π}{8}$ $(8pi)/8$ radians)
Therefore, the supplement of the angle at the 3rd corner would simply be the sum of the measures of the other two, which would be $\frac{6 π}{8}$ $(6pi)/8$ , or $\frac{3 π}{4}$ $(3pi)/4$ .

The complement is similar. We can easily see that the measure of the unmentioned angle is $\frac{2 π}{8}$ $(2pi)/8$ radians, and therefore its complement is $\frac{4 π}{8} - \frac{2 π}{8}$ $(4pi)/8 - (2pi)/8$ , which is equal to $\frac{2 π}{8}$ $(2pi)/8$ , or $\frac{π}{4}$ $pi/4$ .

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A triangle has two corners of angles $\frac{π}{8}$ $pi /8$ and $\frac{5 π}{8}$ $(5pi)/8$ . What are the complement and supplement of the third corner?

1 Answer

Explanation:

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A triangle has two corners of angles π8pi /8 and 5π8(5pi)/8 . 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 $\frac{5 π}{8}$ $(5pi)/8$ . What are the complement and supplement of the third corner?