A triangle has two corners of angles #pi /8# and #(5pi)/6 #. What are the complement and supplement of the third corner?

Answer 1

Complementary angle: #11/24pi#

Supplementary angle: #23/24pi#

Things to Remember [1] The sum of the 3 interior angles of a triangle #=pi# [2] Complementary angles add up to #pi/2# [3] Supplementary angles add up to #pi#
Given two angles #pi/8# and #(5pi)/6# the third angle must be #color(white)("XXX")=pi-(pi/8+(5pi)/6)#
#color(white)("XXX")=pi-((3pi+20pi)/24)#
#color(white)("XXX")=pi/24#
Complement of the third angle #=pi/2-pi/24= (11pi)/24#
Supplement of the third angle #=pi-pi/24=(23pi)/24#
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Answer 2

To find the complement and supplement of the third angle in the triangle, we need to first calculate the measure of the third angle using the fact that the sum of angles in a triangle is always π radians (180 degrees). Then, we can find the complement and supplement of that angle.

Given angles:

  1. π/8
  2. 5π/6

Let x be the measure of the third angle.

Using the fact that the sum of angles in a triangle is π radians:

π/8 + 5π/6 + x = π

Solving for x:

x = π - π/8 - 5π/6

x = π - (3π/24 + 20π/24)

x = π - 23π/24

x = π(24/24) - 23π/24

x = (24π/24) - (23π/24)

x = π/24

The measure of the third angle is π/24 radians.

Complement of the third angle: Complement = π/2 - π/24

Complement = (12π/24) - (1π/24)

Complement = 11π/24

Supplement of the third angle: Supplement = π - π/24

Supplement = (24π/24) - (1π/24)

Supplement = 23π/24

Therefore, the complement of the third angle is 11π/24 radians, and the supplement of the third angle is 23π/24 radians.

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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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