1. The problem involves constructing a circle with center E, diameter DW, radius EL, and examining angles and arcs related to these points. 2. We start by drawing circle with center E. Label the diameter endpoints as D and W. 3. Draw radius EL. We consider angle \(\angle LEW\) formed at center E between points L and W. 4. Measure the intercepted arc \(\overset{\frown}{LW}\) on the circle, which spans points L and W. 5. Draw segment LD and measure \(\angle LDW\) formed at D by points L and W. 6. Definitions: - \(\angle LEW\) is a central angle because its vertex is at the center E. - \(\overset{\frown}{LW}\) is the arc intercepted by the central angle \(\angle LEW\). - \(\angle LDW\) is an inscribed angle since its vertex is on the circle at point D. 7. Relationship between \(\angle LEW\) and \(\overset{\frown}{LW}\): The measure of a central angle equals the measure of its intercepted arc. 8. Relationship between \(\angle LDW\) and \(\overset{\frown}{LW}\): An inscribed angle measures half the intercepted arc. Final answers: - \(\angle LEW\) is a central angle. - \(\overset{\frown}{LW}\) is the intercepted arc by \(\angle LEW\). - \(\angle LDW\) is an inscribed angle. - Measure \(\angle LEW = \) measure of \(\overset{\frown}{LW}\). - Measure \(\angle LDW = \frac{1}{2}\) measure of \(\overset{\frown}{LW}\).