How to find the angle for a percentage of a circle

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Math › How to find the angle for a percentage of a circle

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Arcs

$m \angle AXC = 135^{\circ }$ ; $arc\ \widehat{AB} = 24^{\circ }$ ; $arc\ \widehat{AC} = 94^{\circ }$

Find the degree measure of $arc\ \widehat{CD}$ .

$66^{\circ }$

Not enough information is given to answer this question.

$164^{\circ}$

$82^{\circ}$

$132^{\circ }$

Explanation

When two chords of a circle intersect, the measure of the angle they form is half the sum of the measures of the arcs they intercept. Therefore,

$m \angle AXB = \frac{m; \widehat{AB} + m; \widehat{CD} }{2}$

Since $\angle AXB$ and $\angle AXC$ form a linear pair, $m \angle AXB + m \angle AXC = 180$ , and $m \angle AXB = 180 - m \angle AXC = 180 - 135 = 45^{\circ }$ .

Substitute $m; \widehat{AB} = 24$ and $m \angle AXB = 45$ into the first equation:

$45 = \frac{24 + m; \widehat{CD} }{2}$

$90 =24 + m; \widehat{CD}$

$66 = m; \widehat{CD}$

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.

$360 \cdot 0.90=324$

Generalsector

What is the angle measure of in the figure above if the sector comprises 37% of the circle?

Explanation

It is very easy to compute the angle of a sector if we know what it is as a percentage of the total circle. To do this, you merely need to multiply by ˚. This yields ˚.

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.

$360 \cdot 0.45=162$

Generalsector

What is the angle measure of in the figure above if the sector comprises % of the circle?

Explanation

It is very easy to compute the angle of a sector if we know what it is as a percentage of the total circle. To do this, you merely need to multiply by ˚. This yields ˚.

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