6. \( \overparen{L W} \) is the intercepted arc of \( \angle L D W \). Compare the measure of \( \angle L D W \) with the degree measure of \( \overparen{L W} \). What statements can you make?

To compare the measure of \( \angle L D W \) with the degree measure of the intercepted arc \( \overparen{L W} \), we can use the properties of angles and arcs in a circle. 1. **Understanding the Relationship**: - The measure of an angle formed by two chords in a circle (like \( \angle L D W \)) is equal to half the measure of the intercepted arc. In this case, the intercepted arc is \( \overparen{L W} \). 2. **Mathematical Representation**: - Let \( m(\angle L D W) \) be the measure of the angle \( L D W \). - Let \( m(\overparen{L W}) \) be the measure of the intercepted arc \( L W \). - According to the property mentioned, we have: \[ m(\angle L D W) = \frac{1}{2} m(\overparen{L W}) \] 3. **Conclusion**: - From the equation, we can conclude that the measure of the angle \( L D W \) is always half the measure of the intercepted arc \( L W \). - Therefore, we can state: - \( m(\angle L D W) < m(\overparen{L W}) \) if \( m(\overparen{L W}) > 0 \). - If \( m(\overparen{L W}) = 0 \), then \( m(\angle L D W) = 0 \). In summary, the measure of \( \angle L D W \) is always half the degree measure of the intercepted arc \( \overparen{L W} \).