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High School Math : How to find the angle for a percentage of a circle

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Example Questions

Example Question #1 : Circles

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

Possible Answers:

Correct answer:

Explanation:

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:

7200=100x

Solve for :

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

72=x

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Example Question #2 : Circles

Arcs

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

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

Possible Answers:

$66^{\circ }$

Not enough information is given to answer this question.

$132^{\circ }$

$82^{\circ}$

$164^{\circ}$

Correct answer:

$66^{\circ }$

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:

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

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

$66 = m\; \widehat{CD}$

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High School Math : How to find the angle for a percentage of a circle

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Circles

Example Question #2 : Circles

All High School Math Resources

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