Move point C so that it lies somewhere INSIDE your circle (but is not at the center of the circle).[br][br]Using the calculated measure of the angle the the calculated measures of the intercepted arcs, hypothesis a formula for finding the measure of any angle INSIDE a circle.[br][br]Move point C again to test your formula.
Write a formula to calculate the measure of INSIDE Angle A, with intercepted arcs BC and DF.
measure Angle A = (BC + DF) / 2[br][br]i.e. if BC = 60° and DF = 40°, [br] then measure Angle A = (60+40)/2 = 50°
Move point C so that it lies somewhere OUTSIDE your circle (but is not at the center of the circle).[br][br]Using the calculated measure of the angle the the calculated measures of the intercepted arcs, hypothesis a formula for finding the measure of any angle INSIDE a circle.[br][br]Move point C again to test your formula.
Write a formula to calculate the measure of OUTSIDE Angle A, with intercepted arcs BC and DF.
measure Angle A = (BC - DF) / 2[br][br]i.e. if BC = 60° and DF = 40°, [br] then measure Angle A = (60 - 40)/2 = 10°
Using the calculated measure of the angles the the calculated measures of their intercepted arcs, hypothesis a formula for finding the measure of any angle ON a circle.[br][br]Move point C again to test your formula.
Write a formula to calculate the measure of ON Angle CDF, with intercepted arc CD.[br][br]What angle formula does this remind you of?
measure Angle CDF = (CD) / 2[br][br]i.e. if CD = 120° [br] then measure Angle CDF = (120)/2 = 60°[br][br][br]This angle measure is calculated the same way we would calculate the measure of an inscribed angle.