Each of those angles are Inscribed angles. A useful fact is that the measure of the intercepted arc of an inscribed angle is twice the measure of the angle.
The intercepted arc of ∠C is arc BED. The intercepted arc of ∠E is arc BCD.
m(arc BED) + m(arc BCD) = 2( m∠C + m∠E)
The two arcs combined make u p the entire circle, so the sum of their measures is 360.
She is not correct, because $3.00 divided by 6 is 50 cents, so by using that equation she could evaluate that she is wrong and find the correct answer.