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)

f-d%3A3be91ca0626641e19f262caa83422d27cc63e8d1f158b0d5845cd1d8%2BIMAGE%2BIMAGE.1.png

Example: Find the value of x.

Geom_13L_fig12

Solution: 

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

Still need help finding the measure of an arc inscribed by an angle? Download Yup and get help from an expert math tutor 24/7.