# A triangle has two corners of angles #pi /12# and #pi/6 #. What are the complement and supplement of the third corner?

Complementary of third angle

Supplementary of third angle

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The sum of the angles in any triangle is always ( \pi ) radians (or 180 degrees).

Given: Angle 1: ( \frac{\pi}{12} ) Angle 2: ( \frac{\pi}{6} )

To find the measure of the third angle, ( \theta ), use the fact that the sum of the angles in a triangle is ( \pi ):

[ \frac{\pi}{12} + \frac{\pi}{6} + \theta = \pi ]

First, find a common denominator for ( \frac{\pi}{12} ) and ( \frac{\pi}{6} ), which is ( \frac{\pi}{12} ).

[ \frac{\pi}{12} + \frac{2\pi}{12} + \theta = \pi ] [ \frac{3\pi}{12} + \theta = \pi ] [ \frac{\pi}{4} + \theta = \pi ]

Now, solve for ( \theta ):

[ \theta = \pi - \frac{\pi}{4} ] [ \theta = \frac{3\pi}{4} ]

The complement of ( \frac{3\pi}{4} ) is the angle that, when added to ( \frac{3\pi}{4} ), equals ( \pi ). Therefore, the complement is ( \frac{\pi}{4} ).

The supplement of ( \frac{3\pi}{4} ) is the angle that, when added to ( \frac{3\pi}{4} ), equals ( 2\pi ). Therefore, the supplement is ( \frac{5\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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