Question

A triangle has two corners of angles `pi /8` and `(pi)/4`. What are the complement and supplement of the third corner?

Answer 1

Complement is `-22.5^circ`

Supplement is `67.5^circ`

Explanation:

Note: `pi` in radians measure equals `180^circ`

We need to find the value of the angles `pi/8` and `pi/4`

`color(orange)(pi/8=180/8=22.5^circ`

`color(brown)(pi/4=180/4=45^circ`

Our next step is to find the third angle of the triangle. For that, we use the rule `color(blue)("Sum of the angles of a triangle is"` `color(blue)(180^circ`

So,

`rarr22.5^circ+45^circ+"Third angle"=180^circ`

`rarr67.5^circ+"Third angle"=180^circ`

`rarr"Third angle"=180^circ-67.5^circ`

`color(green)(rArr"Third angle"=112.5^circ`

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Now we have come to the last step. We need to find the supplement and complement of `112.5^circ`

Let's recall

`color(violet)("Complement of an angle " x^circ=90^circ-x^circ`

`color(purple)("Supplement of an angle " x^circ=180^circ-x^circ`

So,

`"Complement"=90^circ-112.5^circ=-22.5^circ`

`"Supplement"=180^circ-112.5^circ=67.5^circ`

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Therefore, the Complement is `color(green)(-22.5^circ` and the Supplement is `color(green)(67.5^circ`

Hope this helps!!! :)