Geometry - How to find the angle for a percentage of a circle

If you have percent of a circle, what is the angle, in degrees, that creates that region?

Explanation

A full circle has 360 degrees, which means that 100% of the circle is 360 degrees.

Now you need to convert into a decimal.

$66.7% \rightarrow \frac{66.7}{100}=0.667$

If you multiply 360 by 0.667, you get the degree measure that corresponds to the percentage, which is 240.

$360 \cdot 0.667=240$

If you have of a circle, what is the angle, in degrees, that creates that region?

Explanation

A full circle has 360 degrees, which means that 100% of the circle is 360 degrees.

First convert into a decimal.

$20% \rightarrow \frac{20}{100}=0.2$

If you multiply 360 by 0.20, you get the degree measure that corresponds to the percentage, which is 72.

$360 \cdot 0.2=72$

If you have of a circle, what is the angle, in degrees, that creates that region?

Explanation

A full circle has 360 degrees, which means that 100% of the circle is 360 degrees.

In order to start this problem we need to convert the percent into a decimal.

$30% \rightarrow \frac{30}{100}=0.3$

If you multiply 360 by 0.30, you get the degree measure that corresponds to the percentage, which is 108.

$360\cdot 0.3=108$

A sector contains $\small 12.5%$ of a circle. What is the measure of the central angle of the sector?

$\small 45^\circ$

$\small 30^\circ$

$\small 12.5^\circ$

$\small 22.5^\circ$

$\small 8^\circ$

Explanation

An entire circle is $\small 360^\circ$ . A sector that is $\small 12.5%$ of the circle therefore has a central angle that is $\small 12.5%$ of $\small 360^\circ$ .

$\small 12.5%(360)=45$

Therefore, our central angle is $\small 45^\circ$

If you have of a circle, what is the angle, in degrees, that creates that region?

Explanation

A full circle has 360 degrees, which means that 100% of the circle is 360 degrees.

First convert the percent to decimal.

$35% \rightarrow \frac{35}{100}=0.35$

Now if you multiply 360 by 0.35, you get the degree measure that corresponds to the percentage, which is 126.

$360 \cdot 0.35=126$

If you have of a circle, what is the angle, in degrees, that creates that region?

Explanation

A full circle has 360 degrees, which means that 100% of the circle is 360 degrees.

First convert the percentage into a decimal.

$90% \rightarrow \frac{90}{100}=0.9$

If you multiply 360 by 0.90, you get the degree measure that corresponds to the percentage, which is 324.

$360 \cdot 0.90=324$

If you have of a circle, what is the angle, in degrees, that creates that region?

Explanation

A full circle has 360 degrees, which means that 100% of the circle is 360 degrees.

First we need to convert the percentage into a decimal.

$45% \rightarrow \frac{45}{100}=0.45$

If you multiply 360 by 0.45, you get the degree measure that corresponds to the percentage, which is 162.

$360 \cdot 0.45=162$

If you have of a circle, what is the angle, in degrees, that creates that region?

Explanation

A full circle has 360 degrees, which means that 100% of the circle is 360 degrees.

In order to solve this problem we first need to convert the percentage into a decimal.

$37.5% \rightarrow \frac{37.5}{100}=0.375$

If you multiply 360 by 0.375, you get the degree measure that corresponds to the percentage, which is 135.

$360 \cdot 0.375=135$

If you have of a circle, what is the angle, in degrees, that creates that region?

Explanation

A full circle has 360 degrees, which means that 100% of the circle is 360 degrees.

First we need to convert the percentage into a decimal.

$70% \rightarrow \frac{70}{100}=0.7$

If you multiply 360 by 0.70, you get the degree measure that corresponds to the percentage, which is 252.

$360 \cdot 0.7 =252$

How many degrees are in of a circle?

$126^{\circ}$

$95^{\circ}$

$135^{\circ}$

$108^{\circ}$

$75^{\circ}$

Explanation

There are degrees in a circleso the equation to solve becomes a simple percentage problem:

$x=0.35\cdot 360 = 126$

How to find the angle for a percentage of a circle

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