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

Answer 1

Complement of third angle is #pi/24#

and supplement of third angle is #(13pi)/24#

As the two corners of angles are #pi/6# and #(3pi)/8# and sum of angles of a triangle is #pi#
the third angle is #color(white)(XXXX)pi-pi/6-(3pi)/8#
= #(24pi-4pi-9pi)/24=(11pi)/24#
Sum of complementary angle is #pi/2# and sum of supplementary angle is #pi#
Hence complement of third angle, which is #(11pi)/24# is
#pi/2-(11pi)/24=(12pi-11pi)/24=pi/24#

and supplement of third angle is

#pi-(11pi)/24=(24pi-11pi)/24=(13pi)/24#
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Answer 2

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 ).

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

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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Answer from HIX Tutor

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.

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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