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High School Math : Angles

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Example Question #1 : Angles

Solve for and .

(Figure not drawn to scale).

Possible Answers:

$\small x=15^o;\ y=37.5^o$

$\small x=7.5^o;\ y=18.75^o$

$\small x=15^o;\ y=52.5^o$

$\small x=15^o;\ y=7.5^o$

Correct answer:

$\small x=15^o;\ y=37.5^o$

Explanation:

The angles containing the variable all reside along one line, therefore, their sum must be 180^o .

$\small 5x+4x+3x=180^o$

$\small 12x=180^o$

$\small x=15^o$

Because and are opposite angles, they must be equal.

$\small 2y=5x$

$\small x=15^o$

$\small 2y=5(15^o)=75^o$

$\small y=\frac{75^o}{2}=37.5^o$

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Example Question #11 : Trigonometry

Are $73^{\circ}$ and $17^{\circ}$ complementary angles?

Possible Answers:

Not enough information

Yes

Maybe

Correct answer:

Yes

Explanation:

Complementary angles add up to $90^{\circ}$ . Therefore, these angles are complementary.

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Example Question #2 : Angles

What angle is complementary to $34^\circ$ ?

Possible Answers:

$156^\circ$

$146^\circ$

$66^\circ$

$56^\circ$

$34^\circ$

Correct answer:

$56^\circ$

Explanation:

Two complementary angles add up to $90^\circ$ .

Therefore, $34^\circ+x^\circ=90^\circ$ .

$x^\circ=90^\circ-34^\circ$

$x^\circ=56^\circ$

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Example Question #3 : Angles

Which of the following angles is supplementary to $15^\circ$ ?

Possible Answers:

$175^\circ$

$165^\circ$

$75^\circ$

$12^\circ$

$85^\circ$

Correct answer:

$165^\circ$

Explanation:

When two angles are supplementary, they add up to $180^\circ$ .

For this problem, we can set up an equation and solve for the supplementary angle:

$x^\circ+15^\circ=180^\circ$

$x^\circ=180^\circ-15^\circ$

$x^\circ=165^\circ$

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Example Question #4 : Angles

What angle is supplementary to $131^\circ$ ?

Possible Answers:

$140^\circ$

$229^\circ$

$-41^\circ$

$49^\circ$

$41^\circ$

Correct answer:

$49^\circ$

Explanation:

Supplementary angles add up to $180^\circ$ . That means:

$x+131^\circ=180^\circ$

$x=180^\circ-131^\circ$

$x=49^\circ$

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Example Question #2 : Angles

Solve for .

(Figure not drawn to scale).

Possible Answers:

8^o

10^o

12^o

14^o

Correct answer:

14^o

Explanation:

The angles are supplementary, therefore, the sum of the angles must equal 180^o .

$\small (4n+22^o)+(8n-10^o)=180^o$

$\small 4n+22^o+8n-10^o=180^o$

$\small 12n+12^o=180^o$

$\small 12n=168^o$

$\small n=14^o$

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Example Question #3 : Angles

Are $129^{\circ}$ and $51^{\circ}$ supplementary angles?

Possible Answers:

Yes

Not enough information

Correct answer:

Yes

Explanation:

Since supplementary angles must add up to $180^{\circ}$ , the given angles are indeed supplementary.

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Example Question #7 : Angles

Which of the following angles is complementary to $32^\circ$ ?

Possible Answers:

$58^\circ$

$68^\circ$

$48^\circ$

$158^\circ$

$148^\circ$

Correct answer:

$58^\circ$

Explanation:

Two complementary angles add up to $90^\circ$ .

$90^\circ=32^\circ+x^\circ$

$90^\circ-32^\circ=x^\circ$

$58^\circ=x^\circ$

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Example Question #8 : Angles

What angle is supplementary to $142^\circ$ ?

Possible Answers:

$38^\circ$

$48^\circ$

$308^\circ$

$-52^\circ$

$218^\circ$

Correct answer:

$38^\circ$

Explanation:

When two angles are supplementary, they add up to $180^\circ$ .

$142^\circ+x=180^\circ$

Solve for :

$142^\circ+x=180^\circ$

$x=180^\circ-142^\circ$

$x=38^\circ$

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Example Question #1 : Understanding Coterminal Angles

Which of the following angles is coterminal with $\frac{2\pi}{7}$ ?

Possible Answers:

$-\frac{12\pi}{7}$

$\frac{9\pi}{7}$

$\frac{12\pi}{7}$

$-\frac{9\pi}{7}$

$-\frac{2\pi}{7}$

Correct answer:

$-\frac{12\pi}{7}$

Explanation:

For an angle to be coterminal with $\theta$ , that angle must be of the form $\theta + 2\pi N$ for some integer - or, equivalently, the difference of the angle measures multiplied by $\frac{1}{2\pi}$ must be an integer. We apply this test to all five choices.

$\frac{9\pi}{7}$ :

$\left ( \frac{1}{2\pi } \right ) \left ( \frac{2\pi}{7} - \frac{9\pi}{7} \right )$

$=\left ( \frac{1}{2\pi } \right )\left (- \frac{7\pi}{7} \right ) =\left ( \frac{1}{2\pi } \right ) \pi = \frac{1}{2 }$

$\frac{12\pi}{7}$ :

$\left ( \frac{1}{2\pi } \right ) \left ( \frac{2\pi}{7} - \frac{12\pi}{7} \right )$

$=\left ( \frac{1}{2\pi } \right )\left (- \frac{10\pi}{7} \right ) =- \frac{5}{7}$

$-\frac{2\pi}{7}$ :

$\left ( \frac{1}{2\pi } \right ) \left [\frac{2\pi}{7} -\left ( -\frac{2\pi}{7} \right ) \right ]$

$=\left ( \frac{1}{2\pi } \right )\left ( \frac{2\pi}{7} + \frac{2\pi}{7 }\right )$

$=\left ( \frac{1}{2\pi } \right )\left ( \frac{4\pi}{7} \right ) = \frac{2}{7}$

$-\frac{9\pi}{7}$ :

$\left ( \frac{1}{2\pi } \right ) \left [\frac{2\pi}{7} -\left ( -\frac{9\pi}{7} \right ) \right ]$

$=\left ( \frac{1}{2\pi } \right )\left ( \frac{2\pi}{7} + \frac{9\pi}{7 }\right )$

$=\left ( \frac{1}{2\pi } \right )\left ( \frac{11\pi}{7} \right ) = \frac{11}{14 }$

$-\frac{12\pi}{7}$ :

$\left ( \frac{1}{2\pi } \right ) \left [\frac{2\pi}{7} -\left ( -\frac{12\pi}{7} \right ) \right ]$

$=\left ( \frac{1}{2\pi } \right )\left ( \frac{2\pi}{7} + \frac{12\pi}{7 }\right )$

$=\left ( \frac{1}{2\pi } \right )\left ( \frac{14\pi}{7} \right ) = \left ( \frac{1}{2\pi } \right ) \cdot2\pi = 1$

$-\frac{12\pi}{7}$ is the correct choice, since only that choice passes our test.

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High School Math : Angles

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Angles

Example Question #11 : Trigonometry

Example Question #2 : Angles

Example Question #3 : Angles

Example Question #4 : Angles

Example Question #2 : Angles

Example Question #3 : Angles

Example Question #7 : Angles

Example Question #8 : Angles

Example Question #1 : Understanding Coterminal Angles

All High School Math Resources

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