High School Math : Understanding Complementary and Suplmentary Angles

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : Angles

Are \(\displaystyle 73^{\circ}\) and \(\displaystyle 17^{\circ}\) complementary angles?

Possible Answers:

No

Yes

Not enough information

Maybe

Correct answer:

Yes

Explanation:

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

Example Question #1 : Angles

What angle is complementary to \(\displaystyle 34^\circ\)?

Possible Answers:

\(\displaystyle 156^\circ\)

\(\displaystyle 66^\circ\)

\(\displaystyle 146^\circ\)

\(\displaystyle 56^\circ\)

\(\displaystyle 34^\circ\)

Correct answer:

\(\displaystyle 56^\circ\)

Explanation:

Two complementary angles add up to \(\displaystyle 90^\circ\).

Therefore, \(\displaystyle 34^\circ+x^\circ=90^\circ\).

\(\displaystyle x^\circ=90^\circ-34^\circ\)

\(\displaystyle x^\circ=56^\circ\)

Example Question #3 : Angles

Which of the following angles is supplementary to \(\displaystyle 15^\circ\)?

Possible Answers:

\(\displaystyle 85^\circ\)

\(\displaystyle 165^\circ\)

\(\displaystyle 12^\circ\)

\(\displaystyle 175^\circ\)

\(\displaystyle 75^\circ\)

Correct answer:

\(\displaystyle 165^\circ\)

Explanation:

When two angles are supplementary, they add up to \(\displaystyle 180^\circ\).

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

\(\displaystyle x^\circ+15^\circ=180^\circ\)

\(\displaystyle x^\circ=180^\circ-15^\circ\)

\(\displaystyle x^\circ=165^\circ\)

Example Question #1 : Angles

What angle is supplementary to \(\displaystyle 131^\circ\)?

Possible Answers:

\(\displaystyle 41^\circ\)

\(\displaystyle 229^\circ\)

\(\displaystyle -41^\circ\)

\(\displaystyle 49^\circ\)

\(\displaystyle 140^\circ\)

Correct answer:

\(\displaystyle 49^\circ\)

Explanation:

Supplementary angles add up to \(\displaystyle 180^\circ\). That means:

\(\displaystyle x+131^\circ=180^\circ\)

\(\displaystyle x=180^\circ-131^\circ\)

\(\displaystyle x=49^\circ\)

Example Question #4 : Graphing Functions

Solve for \(\displaystyle n\).

Question_2

(Figure not drawn to scale).

Possible Answers:

\(\displaystyle 10^o\)

\(\displaystyle 12^o\)

\(\displaystyle 8^o\)

\(\displaystyle 14^o\)

Correct answer:

\(\displaystyle 14^o\)

Explanation:

The angles are supplementary, therefore, the sum of the angles must equal \(\displaystyle 180^o\).

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

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

\(\displaystyle \small 12n+12^o=180^o\)

\(\displaystyle \small 12n=168^o\)

\(\displaystyle \small n=14^o\)

Example Question #4 : Graphing Functions

Are \(\displaystyle 129^{\circ}\) and \(\displaystyle 51^{\circ}\) supplementary angles?

Possible Answers:

Yes

No

Not enough information

Correct answer:

Yes

Explanation:

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

Example Question #5 : Angles

Which of the following angles is complementary to \(\displaystyle 32^\circ\)?

Possible Answers:

\(\displaystyle 68^\circ\)

\(\displaystyle 58^\circ\)

\(\displaystyle 158^\circ\)

\(\displaystyle 48^\circ\)

\(\displaystyle 148^\circ\)

Correct answer:

\(\displaystyle 58^\circ\)

Explanation:

Two complementary angles add up to \(\displaystyle 90^\circ\).

\(\displaystyle 90^\circ=32^\circ+x^\circ\)

\(\displaystyle 90^\circ-32^\circ=x^\circ\)

\(\displaystyle 58^\circ=x^\circ\)

Example Question #6 : Angles

What angle is supplementary to \(\displaystyle 142^\circ\)?

Possible Answers:

\(\displaystyle 48^\circ\)

\(\displaystyle -52^\circ\)

\(\displaystyle 308^\circ\)

\(\displaystyle 38^\circ\)

\(\displaystyle 218^\circ\)

Correct answer:

\(\displaystyle 38^\circ\)

Explanation:

When two angles are supplementary, they add up to \(\displaystyle 180^\circ\).

\(\displaystyle 142^\circ+x=180^\circ\)

Solve for \(\displaystyle x\):

\(\displaystyle 142^\circ+x=180^\circ\)

\(\displaystyle x=180^\circ-142^\circ\)

\(\displaystyle x=38^\circ\)

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