EXAMPLE 1 Use congruent chords to find an arc measure

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Presentation transcript:

EXAMPLE 1 Use congruent chords to find an arc measure In the diagram, P Q, FG JK , and mJK = 80o. Find mFG SOLUTION Because FG and JK are congruent chords in congruent circles, the corresponding minor arcs FG and JK are congruent. So, mFG = mJK = 80o.

GUIDED PRACTICE for Example 1 Use the diagram of D. 1. If mAB = 110°, find mBC SOLUTION Because AB and BC are congruent chords in the same circle, the corresponding minor arcs AB and BC are congruent. So, mBC = mAB = 110o.

GUIDED PRACTICE for Example 1 Use the diagram of D. 2. If mAC = 150°, find mAB

GUIDED PRACTICE for Example 1 SOLUTION Because AB and BC are congruent chords in the same circle, the corresponding minor arcs AB and BC are congruent. So, mBC = mAB And, mBC + mAB + mAC = 360° So, 2 mAB + mAC = 360° 2 mAB + 150° = 360° Substitute 2 mAB = 360 – 150 Subtract 2 mAB = 210 mAB = 105° Simplify mAB = 105° ANSWER