The measure of arc DF of the circle is option (A) 76°.
What is a circle?
A circle is a collection of all points in a plane which are at a constant distance from a fixed point. A circle is a round-shaped figure that has no corners or edges.
For the given situation,
The diagram shows the circle with center O.
∠ FEO = 38°
The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.
So [tex]\angle FED = \frac{1}{2}arc DF[/tex]
⇒ [tex]38 = \frac{1}{2}arc DF[/tex]
⇒ [tex]38(2) = arc DF[/tex]
⇒ [tex]arc DF=76[/tex]
Hence we can conclude that the measure of arc DF of the circle is option (A) 76°.
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