Inscribed Angle Math Example 3

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Example 3

easy
An inscribed angle measures 35°35°. What is the measure of its intercepted arc?

Solution

  1. 1
    Step 1: Use the Inscribed Angle Theorem in reverse: intercepted arc =2×= 2 \times inscribed angle =2×35°= 2 \times 35°.
  2. 2
    Step 2: Calculate: intercepted arc =70°= 70°.

Answer

70°70°
The inscribed angle is half the intercepted arc, so the intercepted arc is twice the inscribed angle. Multiplying 35° by 2 gives the intercepted arc of 70°.

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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More Inscribed Angle Examples

Example 1 easy

An inscribed angle intercepts an arc of [formula]. What is the measure of the inscribed angle?

Example 2 medium

In circle [formula], inscribed angle [formula] intercepts arc [formula]. If arc [formula], and arc [

Example 4 hard

Quadrilateral [formula] is inscribed in a circle. If [formula], find [formula]. Then, if arc [formul

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