How to find the percentage of a sector from an angle - ACT Math
Card 0 of 5
The sector above represents what percentage of the complete circle? Round to the nearest hundredth.
The sector above represents what percentage of the complete circle? Round to the nearest hundredth.
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 
.
This question is very easy to solve. You merely need to find what percentage
Rounding, you get
Compare your answer with the correct one above
Figure not drawn to scale.
What percentage of the circle is sector 
? Round to the nearest hundredth of a percent.
Figure not drawn to scale.
What percentage of the circle is sector
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 
.
Do not overthink this question! All you need to remember is that a given circle contains
Rounded, this is
Compare your answer with the correct one above
A sector of a circle is bounded by the minor arc of 
. What percentage of the circle is the arc?
A sector of a circle is bounded by the minor arc of
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 fractionthe 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.
The only information provided is that the sector is
Therefore, in order to solve for what percent the sector represents of the entire circle, we need to find out what fractionthe sector makes up of the entire circle. Keep in mind that a circle measures up to
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
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
Compare your answer with the correct one above
A sector of an angle is bounded the major arc of 
. What percent of the circle does this make up?
A sector of an angle is bounded the major arc of
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 fractionthe 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.
The only information provided is that the sector is
Keep in mind that a circle measures
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
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
Compare your answer with the correct one above
In circle 
, central angle 
and inscribed angle 
both intercept minor arc 
. If 
, what is the measure of 
?
In circle
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, 
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
Therefore,
Compare your answer with the correct one above