1. 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.

2. 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.

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

4. 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