25 Percent Of A Circle

All Intermediate Geometry Resources

How many degrees are in $35\%$ of a circle?

Correct respond:

$126^{\circ}$

Explanation:

In that location are 360 degrees in a circleso the equation to solve becomes a uncomplicated percentage problem:

$x=0.35\cdot 360 = 126$

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

Correct reply:

$\small 45^\circ$

Explanation:

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

$\small 12.5\%(360)=45$

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

If y'all have 66.7 percent of a circle, what is the bending, in degrees, that creates that region?

Correct reply:

240

Caption:

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

Now you lot need to catechumen $66.7\%$ into a decimal.

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

If you multiply 360 by 0.667, y'all become the degree measure out that corresponds to the percent, which is 240.

$360 \cdot 0.667=240$

If you take $20\%$ of a circle, what is the angle, in degrees, that creates that region?

Right answer:

Explanation:

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

First convert $20\%$ 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 pct, which is 72.

$360 \cdot 0.2=72$

If you accept $30\%$ of a circumvolve, what is the angle, in degrees, that creates that region?

Correct answer:

108

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 percentage into a decimal.

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

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

$360\cdot 0.3=108$

If you have $35\%$ of a circle, what is the angle, in degrees, that creates that region?

Right answer:

126

Explanation:

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

First catechumen the percent to decimal.

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

At present if you multiply 360 past 0.35, y'all go the degree measure out that corresponds to the percentage, which is 126.

$360 \cdot 0.35=126$

If you lot have $90\%$ of a circle, what is the angle, in degrees, that creates that region?

Correct reply:

324

Explanation:

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

First convert the pct into a decimal.

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

If y'all multiply 360 by 0.ninety, you lot get the degree measure that corresponds to the per centum, which is 324.

$360 \cdot 0.90=324$

If you accept $45\%$ of a circle, what is the angle, in degrees, that creates that region?

Correct answer:

162

Caption:

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

Beginning we need to convert the per centum into a decimal.

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

If you multiply 360 by 0.45, yous become the caste measure that corresponds to the pct, which is 162.

$360 \cdot 0.45=162$

If yous have $37.5\%$ of a circle, what is the angle, in degrees, that creates that region?

Correct answer:

135

Caption:

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

In gild 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 lot get the caste measure that corresponds to the percentage, which is 135.

$360 \cdot 0.375=135$

If you have $70\%$ of a circle, what is the angle, in degrees, that creates that region?

Correct answer:

252

Explanation:

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

Starting time we need to catechumen the percent 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 pct, which is 252.

$360 \cdot 0.7 =252$

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