Finding the Measure of an Arc Intercepted by an Angle

Definition: The measure of an inscribed angle is half of measure of the intercepted arc

Inscribed angle measure = 1/2 (arc measure)


Example: Find the value of x.



To find the value of x, we’ll need to use the formula for finding the measure of an inscribed angle.

Step 1: Plug the given value, 30° into the formula. This will allow us to solve for x, where x equals the measure of the arc AB.
inscribed angle measure = 1/2 (arc measure)
30 = 1/2 (x )

Step 2: Solve for x:
30 = 1/2 (x )
2*30 = x
x = 60
arcAB = 60°

Here we basically used the formula: 2(inscribed angle measure) = arc measure

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