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Trigonometry : Angles

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Example Questions

Example Question #21 : Complementary And Supplementary Angles

Find the complement of $\frac{\pi}{6}$ $\displaystyle \frac{\pi}{6}$ .

Possible Answers:

$\pi$ $\displaystyle \pi$

$\frac{\pi }{2}$ $\displaystyle \frac{\pi }{2}$

$\frac{\pi }{6}$ $\displaystyle \frac{\pi }{6}$

$\frac{\pi }{3}$ $\displaystyle \frac{\pi }{3}$

$\frac{\pi }{4}$ $\displaystyle \frac{\pi }{4}$

Correct answer:

$\frac{\pi }{3}$ $\displaystyle \frac{\pi }{3}$

Explanation:

Two angles are complementary if their sum is 90°. The same is true even for radian measures which are an equivalent way to write degree measures. To find an angle's complement, subtract it from 90° or

$\displaystyle \frac{\pi }{2}$ . Remember, complementary angles are positive.

$\displaystyle \frac{\pi}{2}-\frac{\pi }{6}\rightarrow \frac{3\pi }{6}-\frac{\pi }{6}\rightarrow \frac{2\pi }{6}=\frac{\pi }{3}$

In the middle step we found a common denominator as is custom for subtracting fractions with different denominators.

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Example Question #21 : Angles

Find the supplement of 112°.

Possible Answers:

None of the other answers.

$248^{\circ}$ $\displaystyle 248^{\circ}$

$158^{\circ}$ $\displaystyle 158^{\circ}$

$22^{\circ}$ $\displaystyle 22^{\circ}$

$68^{\circ}$ $\displaystyle 68^{\circ}$

Correct answer:

$68^{\circ}$ $\displaystyle 68^{\circ}$

Explanation:

Two angles are supplementary if their sum is 180°. Thus, to find the supplement of an angle, subtract it from 180°. Remember that supplementary angles are positive angles.

$180^{\circ}-112^{\circ}=68^{\circ}$ $\displaystyle 180^{\circ}-112^{\circ}=68^{\circ}$

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Example Question #22 : Angles

What angle do I add to $50^\circ$ $\displaystyle 50^\circ$ to make the sum complementary?

Possible Answers:

$50^\circ$ $\displaystyle 50^\circ$

$35^\circ$ $\displaystyle 35^\circ$

$40^\circ$ $\displaystyle 40^\circ$

$45^\circ$ $\displaystyle 45^\circ$

Correct answer:

$40^\circ$ $\displaystyle 40^\circ$

Explanation:

Step 1: Define complementary angles.

Complementary angles are two angles that must always add up to 90.

Step 2: Find the other angle:

The sum must be 90, so subtract the given angle from the sum to find the missing angle:

$90^\circ-50^\circ=40^\circ$ $\displaystyle 90^\circ-50^\circ=40^\circ$

The missing angle is $40^\circ$ $\displaystyle 40^\circ$

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Example Question #23 : Angles

What must the sum of two angles be, given that the angles are supplementary to each other?

Possible Answers:

100 $\displaystyle 100$

180 $\displaystyle 180$

360 $\displaystyle 360$

140 $\displaystyle 140$

Correct answer:

180 $\displaystyle 180$

Explanation:

Step 1: Define Supplementary angles. The answer is in the definition:

Two angles, if they are Supplementary to each other, their sum must equal $\displaystyle 180$ degrees.

The sum of the angles must be $180^\circ$ $\displaystyle 180^\circ$

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Example Question #21 : Angles

Find the complementary angle of $20^{\circ}$ $\displaystyle 20^{\circ}$

Possible Answers:

$160^{\circ}$ $\displaystyle 160^{\circ}$

$-20^{\circ}$ $\displaystyle -20^{\circ}$

$25^{\circ}$ $\displaystyle 25^{\circ}$

$70^{\circ}$ $\displaystyle 70^{\circ}$

$340^{\circ}$ $\displaystyle 340^{\circ}$

Correct answer:

$70^{\circ}$ $\displaystyle 70^{\circ}$

Explanation:

To find the complementary angle of x, you need to subtract x from 90 degrees.

$Complementary = 90^{\circ} -x$ $\displaystyle Complementary = 90^{\circ} -x$

So, since we are trying to find the complementary angle of 20 degrees, we have:

$90^{\circ}-20^{\circ}=70^{\circ}$ $\displaystyle 90^{\circ}-20^{\circ}=70^{\circ}$

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Example Question #21 : Complementary And Supplementary Angles

Find the complementary angle of $68.2^{\circ}$ $\displaystyle 68.2^{\circ}$

Possible Answers:

$111.8^{\circ}$ $\displaystyle 111.8^{\circ}$

$21.8^{\circ}$ $\displaystyle 21.8^{\circ}$

$31.8^{\circ}$ $\displaystyle 31.8^{\circ}$

$391.8^{\circ}$ $\displaystyle 391.8^{\circ}$

$-68.2^{\circ}$ $\displaystyle -68.2^{\circ}$

Correct answer:

$21.8^{\circ}$ $\displaystyle 21.8^{\circ}$

Explanation:

To find the complementary angle of x, you need to subtract x from 90 degrees.

$Complementary = 90^{\circ} -x$ $\displaystyle Complementary = 90^{\circ} -x$

Since we are trying to find the complementary angle of 68.2 degrees, we have:

$90^{\circ}-68.2^{\circ}=21.8^{\circ}$ $\displaystyle 90^{\circ}-68.2^{\circ}=21.8^{\circ}$

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Example Question #24 : Angles

Find the Complementary angle of $\frac{\pi}{3}$ $\displaystyle \frac{\pi}{3}$ :

Possible Answers:

$\frac{2\pi}{3}$ $\displaystyle \frac{2\pi}{3}$

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

$\frac{\pi}{4}$ $\displaystyle \frac{\pi}{4}$

$\frac{\pi}{6}$ $\displaystyle \frac{\pi}{6}$

$\frac{\pi}{2}$ $\displaystyle \frac{\pi}{2}$

Correct answer:

$\frac{\pi}{6}$ $\displaystyle \frac{\pi}{6}$

Explanation:

SInce the given angle is in radians to find the Complementary angle we need to subtract the giving angle from $\frac{\pi}{2}$ $\displaystyle \frac{\pi}{2}$ . Hence,

$\frac{\pi}{2}-\frac{\pi}{3}=\frac{\pi}{6}$ $\displaystyle \frac{\pi}{2}-\frac{\pi}{3}=\frac{\pi}{6}$

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Example Question #25 : Angles

Find the Complementary angle of $\frac{\pi}{7}$ $\displaystyle \frac{\pi}{7}$ :

Possible Answers:

$\frac{5\pi}{14}$ $\displaystyle \frac{5\pi}{14}$

$\frac{3\pi}{7}$ $\displaystyle \frac{3\pi}{7}$

89.55

$\frac{\pi}{2}$ $\displaystyle \frac{\pi}{2}$

$\frac{6\pi}{7}$ $\displaystyle \frac{6\pi}{7}$

Correct answer:

$\frac{5\pi}{14}$ $\displaystyle \frac{5\pi}{14}$

Explanation:

SInce the given angle is in radians to find the Complementary angle we need to subtract the giving angle from $\frac{\pi}{2}$ $\displaystyle \frac{\pi}{2}$ . Hence,

$\frac{\pi}{2}-\frac{\pi}{7}=\frac{5\pi}{14}$ $\displaystyle \frac{\pi}{2}-\frac{\pi}{7}=\frac{5\pi}{14}$

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Example Question #26 : Angles

Find the Supplementary angle of $40^{\circ}$ $\displaystyle 40^{\circ}$

Possible Answers:

$-40^{\circ}$ $\displaystyle -40^{\circ}$

$60^{\circ}$ $\displaystyle 60^{\circ}$

$320^{\circ}$ $\displaystyle 320^{\circ}$

$140^{\circ}$ $\displaystyle 140^{\circ}$

$50^{\circ}$ $\displaystyle 50^{\circ}$

Correct answer:

$140^{\circ}$ $\displaystyle 140^{\circ}$

Explanation:

Since we are trying to find the supplementary angle of 40 degrees, we have to:

$\textup{Angle}_1+\textup{Angle}_2=180^\circ$

$180^{\circ}-40^{\circ}=140^{\circ}$ $\displaystyle 180^{\circ}-40^{\circ}=140^{\circ}$

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Example Question #21 : Complementary And Supplementary Angles

Find the Supplementary angle of $92.67^{\circ}$ $\displaystyle 92.67^{\circ}$

Possible Answers:

$-92.67^{\circ}$ $\displaystyle -92.67^{\circ}$

$2.67^{\circ}$ $\displaystyle 2.67^{\circ}$

$87.33^{\circ}$ $\displaystyle 87.33^{\circ}$

The supplementary angle of $92.67^{\circ}$ $\displaystyle 92.67^{\circ}$ does not exist, because the angle is larger than $90^{\circ}$ $\displaystyle 90^{\circ}$ .

$267.33^{\circ}$ $\displaystyle 267.33^{\circ}$

Correct answer:

$87.33^{\circ}$ $\displaystyle 87.33^{\circ}$

Explanation:

Since we are trying to find the supplementary angle of 92.67 degrees, we have to:

$\textup{Angle}_1+\textup{Angle}_2=180^\circ$

$180^{\circ}-92.67^{\circ}=87.33^{\circ}$ $\displaystyle 180^{\circ}-92.67^{\circ}=87.33^{\circ}$

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Trigonometry : Angles

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #21 : Complementary And Supplementary Angles

Example Question #21 : Angles

Example Question #22 : Angles

Example Question #23 : Angles

Example Question #21 : Angles

Example Question #21 : Complementary And Supplementary Angles

Example Question #24 : Angles

Example Question #25 : Angles

Example Question #26 : Angles

Example Question #21 : Complementary And Supplementary Angles

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