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Angle DEF is an inscribed angle on a circle, and m∠DEF = 64°. What is the measure of arc DF?

116°

64°

32°

128°
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128°

Step-by-step explanation:

The measure of an inscribed angle is half the measure of the intercepted arc. That means that the intercepted arc is two times the inscribed angle.

Measure of the inscribed angle DEF is 64°, that means that the measure of the intercepted arc DF is 2×64°, which is 128°.

[tex]m\overset{\huge\frown}{DF} = 2 \times m\angle DE F = 2 \times 64^\circ = 128^\circ[/tex]
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