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.

SOLUTION

Because AB and BC are congruent chords in the same circle, the corresponding minor arcs AB and BC are congruent.

1. If mAB = 110°, find mBC

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.

Subtract

Substitute

mAB = 105° Simplify

So, mBC = mAB

And, mBC + mAB + mAC = 360°

So, 2 mAB + mAC = 360° 2 mAB + 150° = 360°

2 mAB = 360 – 150 2 mAB = 210

mAB = 105° ANSWER