Answer: 72 degrees
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Explanation:
Use the inscribed angle theorem to go from inscribed angle D = 66 to 2*66 = 132. The central angle is double that of its corresponding inscribed angle.
This means arc ABC has measure 132 degrees.
The minor arc BC is 97 degrees, so
(minor arc AB) + (minor arc BC) = arc ABC
(minor arc AB) + (97) = 132
minor arc AB = 132-97
minor arc AB = 35
and
(minor arc DA) + (minor arc AB) = arc DAB
(109) + (35) = arc DAB
144 = arc DAB
arc DAB = 144
Now use the inscribed angle theorem again. Cut the arc measure DAB in half to get its corresponding inscribed angle measure (angle C)
144/2 = 72
angle C is 72 degrees
