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Answer:
【Explanation】:
1. The question revolves around the properties of circles, specifically involving a circle's center, radii, diameters, inscribed angles, and arcs. It involves geometric constructions and measurements.
2. The measure of ∠LEW is being asked in the context of a circle with center E, where EL is a radius and EW is a diameter. Since EW is a diameter, it forms a straight line, and EL being a radius perpendicular to this diameter forms a right angle with it. Therefore, ∠LEW is a right angle.
3. The degree measure of LW is asked. In a circle, the length of an arc is not measured in degrees but rather in linear units. However, the question might be inquiring about the angular measure of the arc LW, which, if LW is a diameter, would be 180 degrees as it represents a semi-circle.
4. ∠LDW is an angle formed by connecting point L (on the circle) with the endpoints of a diameter DW. Since one of the properties of a circle is that an angle formed by a diameter and a point on the circle (inscribed angle) measures half the angle of the semi-circle, ∠LDW measures 90 degrees.
5. An inscribed angle in a circle is defined as an angle whose vertex is on the circle and whose sides contain chords of the circle. The angle ∠LDW is an example of an inscribed angle.
6. The measure of an inscribed angle (∠LDW) is always half the measure of its intercepted arc (arc LW). If ∠LDW is an inscribed angle that intercepts arc LW, and if LW is a semi-circle (180 degrees), then ∠LDW would be half of that, which is 90 degrees.
【Answer】:
1. 90°
2. 180° (if referring to the angular measure of the semi-circle arc LW)
3. 90°
4. An inscribed angle is an angle with its vertex on the circle and sides containing chords of the circle.
5. The measure of ∠LDW is half the degree measure of the intercepted arc LW.
Step-by-step explanation:
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