# A triangle has two corners of angles #pi /12# and #(2pi)/3 #. What are the complement and supplement of the third corner?

Refer to the explanation.

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The complement of an angle is the difference between that angle and a right angle (( \frac{\pi}{2} ) radians or 90 degrees). The supplement of an angle is the difference between that angle and a straight angle (( \pi ) radians or 180 degrees).

Given that the two given angles are ( \frac{\pi}{12} ) and ( \frac{2\pi}{3} ), to find the third angle:

- The sum of the angles in a triangle is ( \pi ) radians (180 degrees).
- Subtract the measures of the two given angles from ( \pi ) to find the measure of the third angle.
- Compute both the complement and supplement of the third angle.

Let ( \theta ) be the measure of the third angle.

[ \theta = \pi - \left(\frac{\pi}{12} + \frac{2\pi}{3}\right) ]

[ \theta = \pi - \left(\frac{\pi}{12} + \frac{8\pi}{12}\right) ]

[ \theta = \pi - \frac{9\pi}{12} ]

[ \theta = \frac{3\pi}{12} ]

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

The complement of ( \frac{\pi}{4} ) is ( \frac{\pi}{2} - \frac{\pi}{4} = \frac{\pi}{4} ).

The supplement of ( \frac{\pi}{4} ) is ( \pi - \frac{\pi}{4} = \frac{3\pi}{4} ).

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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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