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Answer:
- DF = 75°
- FBE = 105°
- FC = 60°
- CBE = 45°
- DAC = 225°
- ABE = 135°
- AFE = 225°
- ABF = 120°
Explanation:
AC and DE are diameters, so divide the circle into equal portions that have a total angle measure of 180°.
angle ABD = 180° -angle DBF - angle FBC = 180° -75° -60°
angle ABD = 45°
angle CBE is a vertical angle to angle ABD, so has the same measure, 45°.
angle ABE is supplementary to angle CBE, so has measure 180° -45° = 135°. Long arc AE is 360° less this value, so is 360° -135° = 225°. Vertical angle DBC has the same measure as angle ABE, so long arc DAE will also be 225°.
angles FBC and CDE add to make angle FBE, so that angle is ...
angle FBE = 60° +45° = 105°