Inscribed Angle Math Example 1

Follow the full solution, then compare it with the other examples linked below.

easy

An inscribed angle intercepts an arc of

80°

. What is the measure of the inscribed angle?

1
Step 1: Recall the Inscribed Angle Theorem: an inscribed angle equals half the intercepted arc. That is, $\angle = \frac{1}{2} \times \text{arc}$ .
2
Step 2: Substitute the intercepted arc measure: $\angle = \frac{1}{2} \times 80°$ .
3
Step 3: Compute the result: $\angle = 40°$ .

Answer

40°

The Inscribed Angle Theorem states that an inscribed angle is exactly half the measure of its intercepted arc. Here, half of 80° gives 40°.

About Inscribed Angle

An angle whose vertex lies on the circle and whose sides are chords of the circle. Its measure is exactly half the measure of the intercepted arc.

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