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

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Question

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

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

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Answer

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}$

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

$66 = m; \widehat{CD}$

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Question

A sector comprises 20% of a circle. What is the central angle of the sector?

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Answer

Proporations can be used to solve for the central angle. Let equal the angle of the sector.

$\frac{20}{100}$=\frac{x}{360}$

Cross mulitply:

Solve for :

$\frac{7200}{100}$=\frac{100x}{100}$

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Question

How many degrees are in of a circle?

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Answer

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

$x=0.35\cdot 360 = 126$

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Question

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

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Answer

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 $\small 45^\circ$

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Question

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

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Answer

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.

$360 \cdot 0.667=240$

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Question

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

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Answer

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.

$360 \cdot 0.2=72$

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Question

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

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Answer

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.

$360\cdot 0.3=108$

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Question

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

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Answer

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.

$360 \cdot 0.35=126$

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Question

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

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Answer

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.

$360 \cdot 0.90=324$

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Question

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

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Answer

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.

$360 \cdot 0.45=162$

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Question

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

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Answer

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.

$360 \cdot 0.375=135$

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Question

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

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Answer

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.

$360 \cdot 0.7 =252$

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Question

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

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Answer

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.

$80% \rightarrow $\frac{80}{100}$=0.8$

If you multiply 360 by 0.80, you get the degree measure that corresponds to the percentage, which is 288.

$360 \cdot 0.8= 288$

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Question

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

Tap to reveal answer

Answer

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

First convert the percentage into a decimal.

$44% \rightarrow $\frac{44}{100}$=0.44$

If you multiply 360 by 0.44, you get the degree measure that corresponds to the percentage, which is 158.4.

$360 \cdot 0.44=158.4$

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Question

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

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Answer

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

First convert the percentage into a decimal.

$18% \rightarrow $\frac{18}{100}$=0.18$

If you multiply 360 by 0.18, you get the degree measure that corresponds to the percentage, which is 64.8.

$360 \cdot 0.18=64.8$

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Question

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

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Answer

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

We first need to convert the percentage into a decimal.

$56% \rightarrow $\frac{56}{100}$=0.56$

If you multiply 360 by 0.56, you get the degree measure that corresponds to the percentage, which is 201.6.

$360 \cdot 0.56=201.6$

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Question

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

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Answer

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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Question

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

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Answer

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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Question

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

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Answer

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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Question

How many degrees are in of a circle?

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Answer

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

$x=0.35\cdot 360 = 126$

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