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?

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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 $$ \overparen{L W} $$.
The measure of angle $$ \angle L D W $$ is half the measure of the intercepted arc $$ \overparen{L W} $$.

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?

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