The correct answer is: (Option A) 100
Step-by-step explanation:
There are two methods to solve this problem.
IMPORTANT NOTE: Do not confuse "arc length" with "measure of arc." Measure of arc is actually the central angle's degree size!
Method-1:
Please see the attached image with the answer.
Since D and F are tangent to a circle. It means the lines DE and FE are at 90° with the radius of the circle DO and FO respectively. And sum of inner angles should be equal to 360°.
Now let us find the value of x (in the picture), which is the measure of arc DF:
80° + 90° + x + 90° = 360°
x = 100° (Option A)
Method-2:
Since the whole circle's measure is 360°. Therefore,
The blue arc + DF (green arc) = 360°
Blue arc = 260°
Therefore,
260° + DF (green arc) = 360°
DF (green arc) = 100° (Option A)