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Trigonometry : Complementary and Supplementary Angles

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Example Question #31 : Complementary And Supplementary Angles

Find the supplementary angle of $\frac{\pi}{4}$ :

Possible Answers:

$\frac{3\pi}{4}$

$-\frac{\pi}{4}$

$\frac{7\pi}{4}$

$\frac{\pi}{2}$

$\frac{\pi}{4}$

Correct answer:

$\frac{3\pi}{4}$

Explanation:

Since the given angle is in radians to find the supplementary angle we need to subtract the giving angle from $\pi$ .

Hence,

$\pi-\frac{\pi}{4}=\frac{3\pi}{4}$

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Example Question #32 : Angles

Find the supplementary angle of $\frac{5\pi}{8}$

Possible Answers:

The supplementary angle of $\frac{5\pi}{8}$ does not exist, because $\frac{5\pi}{8}$ is larger than $\frac{\pi}{2}$ .

$\frac{11\pi}{8}$

$\frac{\pi}{8}$

$\frac{3\pi}{8}$

$-\frac{5\pi}{8}$

Correct answer:

$\frac{3\pi}{8}$

Explanation:

Since the given angle is in radians to find the supplementary angle we need to subtract the giving angle from $\pi$ .

Hence,

$\pi-\frac{5\pi}{8}=\frac{3\pi}{8}$

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Example Question #32 : Complementary And Supplementary Angles

What is the supplementary angle to $110\degree$ ?

Possible Answers:

$75\degree$

$60\degree$

$70\degree$

$40\degree$

Correct answer:

$70\degree$

Explanation:

Supplementary angles, by definition, add up to $180\degree$ .

To find the other angle, you set up the equation

$110\degree+x=180\degree$ .

Solving the equation gets

$x=70\degree$ .

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Example Question #34 : Angles

List the complement and the supplement for $\small \frac{\pi}{4}$ .

Possible Answers:

$\small \frac{3\pi}{4}$ and $\frac{7\pi}{4}$

$\small \frac{\pi}{4}$ and $\small \frac {7\pi}{4}$

$\frac{\pi}{4}$ and $\frac{-3\pi}{4}$

$\small \small \frac{5\pi}{4}$ and $\small \frac{-3\pi}{4}$

$\small \frac{\pi}{4}$ and $\small \frac{3\pi}{4}$

Correct answer:

$\small \frac{\pi}{4}$ and $\small \frac{3\pi}{4}$

Explanation:

To find the complement of $\frac{\pi}{4}$ , subtract it from $\frac{\pi}{2}$ , or equivalently, $\frac{2\pi}{4}$ :

$\frac{2\pi}{4} - \frac{\pi}{4} = \frac{1\pi}{4}$

To find the supplement of $\frac{\pi}{4}$ , subtract it from $\pi$ , or equivalently $\frac{4\pi}{4}$ :

$\small \frac{4\pi}{4} - \frac{\pi}{4} = \frac{3\pi}{4}$

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Example Question #35 : Angles

Which angle is $\frac{2}{3}$ its supplement?

Possible Answers:

$\small \frac{3\pi}{10}$

$\small \frac{5\pi}{3}$

$\small \frac{2\pi}{5}$

$\frac{5\pi}{6}$

$\small \frac{6\pi}{5}$

Correct answer:

$\small \frac{2\pi}{5}$

Explanation:

There are many ways to solve this problem. Regardless, we need to know that supplementary angles add together to $\pi$ . To figure out what plus $\frac{2}{3}$ of itself would equal $\pi$ , we can set up this equation:

$\small x + \frac{2}{3}x = \pi$ to combine like terms, create common denominators

$\small \frac{3}{3}x + \frac{2}{3}x = \pi$

$\small \frac{5}{3}x = \pi$ multiply both sides by the reciprocal, $\small \frac{3}{5}$

$\small x = \pi * \frac{3}{5 }$

$\small x = \frac{3\pi}{5}$

Our actual answer is going to be $\small \frac{2}{3}$ of this, since the angle that we are looking for is $\frac{2}{3 }$ of its supplement. In other words, we just found x, and the angle that we are looking for is $\small \frac{2}{3}x$ :

$\small \frac{2}{{\color{DarkOrange} 3}}*\frac{{\color{DarkOrange} 3}\pi}{5} = \frac{2}{1} * \frac{\pi}{5 }= \frac{2\pi}{5}$

Our answer is $\small \frac{2\pi}{5}$ .

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Trigonometry : Complementary and Supplementary Angles

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #31 : Complementary And Supplementary Angles

Example Question #32 : Angles

Example Question #32 : Complementary And Supplementary Angles

Example Question #34 : Angles

Example Question #35 : Angles

All Trigonometry Resources

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