Understanding Complementary and Suplmentary Angles

Help Questions

Math › Understanding Complementary and Suplmentary Angles

Questions 1 - 8

1

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

$56^\circ$

$66^\circ$

$34^\circ$

$146^\circ$

$156^\circ$

Explanation

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

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

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

$x^\circ=56^\circ$

2

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

$49^\circ$

$41^\circ$

$-41^\circ$

$229^\circ$

$140^\circ$

Explanation

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

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

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

$x=49^\circ$

3

Solve for .

(Figure not drawn to scale).

Explanation

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

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

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

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

$\small 12n=168^o$

$\small n=14^o$

4

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

$38^\circ$

$48^\circ$

$-52^\circ$

$218^\circ$

$308^\circ$

Explanation

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

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

Solve for :

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

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

$x=38^\circ$

5

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

Yes

No

Maybe

Not enough information

Explanation

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

6

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

$58^\circ$

$158^\circ$

$68^\circ$

$148^\circ$

$48^\circ$

Explanation

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

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

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

$58^\circ=x^\circ$

7

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

$165^\circ$

$175^\circ$

$85^\circ$

$75^\circ$

$12^\circ$

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:

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

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

$x^\circ=165^\circ$

8

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

Yes

No

Not enough information

Explanation

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

Return to subject