A triangle has two corners of angles #(3pi )/8# and #(7pi)/12 #. What are the complement and supplement of the third corner?

Answer 1

#(11pi)/24,(23pi)/24#

#"the sum of the angles in a triangle "=pi#
#rArr"third angle " =pi-((3pi)/8+(7pi)/12)#
#color(white)(rArr"third angle"x)=pi-(23)/24=pi/24#
#"complement of " pi/24=pi/2-pi/24=(11pi)/24#
#"supplement of " pi/24=pi-pi/24=(23pi)/24#
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Answer 2

To find the complement and supplement of the third angle in the triangle, first, we need to find the measure of the third angle. Since the sum of the angles in a triangle is always 180 degrees (π radians), we can use this information to find the measure of the third angle.

Let x be the measure of the third angle.

Given that the two angles are (3π)/8 and (7π)/12, we can write the equation:

(3π)/8 + (7π)/12 + x = π

Now, solve for x:

(3π)/8 + (7π)/12 + x = π => (9π + 7π + 8x) / 24 = π => (16π + 8x) / 24 = π => 16π + 8x = 24π => 8x = 8π => x = π

So, the measure of the third angle is π radians.

Now, to find the complement and supplement:

Complement of an angle = π/2 - angle measure => Complement of the third angle = π/2 - π = π/2 - π = -π/2 (or 90° - 180°)

Supplement of an angle = π - angle measure => Supplement of the third angle = π - π = π (or 180°)

Therefore, the complement of the third angle is -π/2 radians (or 90 degrees), and the supplement of the third angle is π radians (or 180 degrees).

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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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