Question

Points D, E, and F are on circle C and EF ≅ DF.



What is the measure of ∠CDF?

14°
19°
26°
38°

Answer 1

CDGE is a quadrilateral, and you have 3 of the angles: 90, 76 and 90.
Since the angle sum of a quad is 360, <DCE must be 104.
Circle geo theorem, says <DCE = 2 * <DFE. So < DFE = 52.
Now CDF and CEF are congruent triangles, since we have 2 radii and a given equal base. They are also both isosceles. We can split <DFE in half to get <CFD = 26, and so since CDF is isoceles, <CDF = 26