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

Complement is

Supplement is

So,

Let's recall

So,

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The third angle of the triangle can be found using the fact that the sum of the angles in a triangle is always equal to pi radians (180 degrees). Let's denote the third angle as ( \theta ).

The sum of the angles in a triangle is ( \pi ) radians (180 degrees), so:

[ \frac{\pi}{8} + \frac{\pi}{4} + \theta = \pi ]

[ \frac{3\pi}{8} + \theta = \pi ]

[ \theta = \pi - \frac{3\pi}{8} ]

Now, to find the complement and supplement of ( \theta ):

- Complement: The complement of an angle is what, when added to the given angle, equals ( \frac{\pi}{2} ) radians (90 degrees).

[ \text{Complement of } \theta = \frac{\pi}{2} - \theta ]

- Supplement: The supplement of an angle is what, when added to the given angle, equals ( \pi ) radians (180 degrees).

[ \text{Supplement of } \theta = \pi - \theta ]

Substitute the value of ( \theta ) into these equations to find the complement and supplement:

- Complement:

[ \text{Complement of } \theta = \frac{\pi}{2} - \left( \pi - \frac{3\pi}{8} \right) ]

- Supplement:

[ \text{Supplement of } \theta = \pi - \left( \pi - \frac{3\pi}{8} \right) ]

After simplifying, you'll get the values for the complement and supplement of ( \theta ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- A triangle has two corners of angles #pi /8# and #(pi)/2 #. What are the complement and supplement of the third corner?
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