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How to Find the Interior Angles of a Circle

The measure of the interior angles of a circle, angles with a vertex on the circumference of the circle, must be found to solve many geometry problems. Interior angles of circle problems often give the measure of the arc of the angle and ask to solve for the angle. Other problems give the measure of one of the other interior angles of the circle and ask you to solve for another interior angle. Although there are many types of interior angle problems, many can be solved with just one simple calculation and a string.

String
Scissors
Ruler

Instructions

- 1
  Cut a string that is longer than the circumference of the circle (the length of the edge that surrounds the circle).
- 2
  Place the string along the circumference of the circle so that it precisely overlaps the circumference of the circle. Cut the string so that it has the same length as the circumference of the circle. Measure the length of the cut string with a ruler. Name this measurement "the measured circumference of the circle."
- 3
  Place another string along the circumference of the circle so that its endpoints are aligned with the endpoints of the arc of the interior angle, overlapping the arc of the interior angle. Cut the string so that the string is the exact length of the arc. Measure the length of the cut string. Name this measurement "the measured arc of the interior angle."
- 4
  Divide the "measured arc of the interior angle" by the "measured circumference of the circle." Divide the resultant value by 360 (the number of degrees in circle). Divide this result by 2 to obtain the measure of the interior angle.
- 5
  Repeat the above procedure to find the other interior angles of the circle.

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