### All ACT Math Resources

## Example Questions

### Example Question #1 : Sectors

The sector above represents what percentage of the complete circle? Round to the nearest hundredth.

**Possible Answers:**

**Correct answer:**

This question is very easy to solve. You merely need to find what percentage degrees is in comparison with the whole of degrees for the circle. This is:

or or

Rounding, you get .

### Example Question #1 : How To Find The Percentage Of A Sector From An Angle

Figure not drawn to scale.

What percentage of the circle is sector ? Round to the nearest hundredth of a percent.

**Possible Answers:**

**Correct answer:**

Do not overthink this question! All you need to remember is that a given circle contains degrees. This means that your sector percentage is merely a ratio of the angle to . This is:

or

Rounded, this is .

### Example Question #3 : Sectors

A sector of a circle is bounded by the minor arc of . What percentage of the circle is the arc?

**Possible Answers:**

**Correct answer:**

The only information provided is that the sector is . When finding a percent, it's helpful to remember that percents are a clean way to show fractions—that is, portions—of a whole.

Therefore, in order to solve for what percent the sector represents of the entire circle, we need to find out what fraction* *the sector makes up of the entire circle. Keep in mind that a circle measures up to . This means that the sector is of the total . This can be written out as:

This can be simplified to:

Note that the degrees signs are gone. This is because when you divide degrees by degrees, the units cancel out! This simplified fraction means that was one-fifth of the entire circle. Now, this fraction may be turned into a percent.

In order to go from fractions to percents, it's helpful to keep in mind that decimals are the important intermediate step. That is, as soon as a fraction can be turned into decimal form, it can easily be converted into a percent by multiplying by 100.

That is, the sector makes up of the entire circle.

### Example Question #4 : Sectors

A sector of an angle is bounded the major arc of . What percent of the circle does this make up?

**Possible Answers:**

**Correct answer:**

The only information provided is that the sector is . When finding a percent, it's helpful to remember that percents are a clean way to show fractions—that is portions—of a whole. In order to solve for what percent the sector makes of the entire circle, we need to find out what fraction* *the sector makes up of the entire circle.

Keep in mind that a circle measures degrees. This means that the sector is of the total . This can be written out as:

This can be simplified to:

Note that the degrees signs are gone. This is because when you divide degrees by degrees, the units cancel out! This simplified fraction means that was three-fourths of the entire circle. Now, this fraction may be turned into a percent.

In order to go from fractions to percents, it's helpful to keep in mind that decimals are the important intermediate step. That is, as soon as a fraction can be turned into decimal form, it can easily be converted into a percent by multiplying by .

That is, the sector makes up of the entire circle.

### Example Question #41 : Circles

In circle , central angle and inscribed angle both intercept minor arc . If , what is the measure of ?

**Possible Answers:**

**Correct answer:**

A central angle and the arc it intercepts always have the same angle, and an inscribed angle always has an angle half the measure of the arc it intercepts. Thus, if the central angle measures , the corresponding inscribed angle must measure .

Therefore,