# A triangle has two corners of angles #pi /6# and #(3pi)/8 #. What are the complement and supplement of the third corner?

Complement of third angle is

and supplement of third angle is

and supplement of third angle is

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The sum of the angles in a triangle is always equal to ( \pi ) radians (180 degrees). To find the measure of the third angle, subtract the measures of the two given angles from ( \pi ).

- Complement: ( \pi - \left(\frac{\pi}{6} + \frac{3\pi}{8}\right) )
- Supplement: ( \pi - \left(\frac{\pi}{6} + \frac{3\pi}{8}\right) )

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To find the complement and supplement of the third angle in the triangle, we first need to calculate the measure of the third angle. Since the sum of the angles in a triangle is always ( \pi ) radians (180 degrees), we can find the measure of the third angle by subtracting the measures of the given angles from ( \pi ).

Let's denote the measure of the third angle as ( \theta ). The given angles are ( \frac{\pi}{6} ) and ( \frac{3\pi}{8} ).

To find the measure of the third angle ( \theta ), we use the equation:

[ \theta = \pi - \left( \frac{\pi}{6} + \frac{3\pi}{8} \right) ]

Once we have found ( \theta ), we can calculate its complement and supplement.

The complement of an angle is the difference between ( \pi ) and the angle's measure. [ \text{Complement} = \pi - \theta ]

The supplement of an angle is the difference between ( 2\pi ) and the angle's measure. [ \text{Supplement} = 2\pi - \theta ]

By plugging in the value of ( \theta ) that we found, we can determine the complement and supplement of the third angle.

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