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Answer :
Final answer:
To find the measure of minor arc FH, we subtract the sum of angles GDF and FDE (149 degrees) from the total degrees in a circle (360 degrees), which gives us 211 degrees for arc FH. The correct option is (D).
Explanation:
The problem is essentially finding the measure of minor arc FH in circle D. Since we know that the circle's total degrees is 360, we can find the major arc FHE by adding the provided angles GDF and FDE, which are 83 and 66 degrees, respectively. The sum of these two angles, which is 149 degrees, represents the measure of the major arc since angles at the center of a circle measure the same as the arc they intercept. To find the measure of the minor arc FH, we subtract the measure of arc FHE from the total degrees in a circle.
Therefore, minor arc FH = 360 - 149 = 211 degrees.
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