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

Study concepts, example questions & explanations for High School Math

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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:


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

Cross mulitply:

Solve for :


Example Question #1 : How To Find The Angle For A Percentage Of A Circle





Find the degree measure of .

Possible Answers:

Not enough information is given to answer this question.

Correct 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, 

Since  and  form a linear pair, , and .

Substitute   and  into the first equation:

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