Answer:
m∠HCG = 45°
m∡DF = 105°
Step-by-step explanation:
m∠ECD + m∠ECF + m∠FCG
= 45° + 60° + 75°
= 180°
As angles on a straight line always sum to 180°, we can conclude that the line DG is a straight line and the diameter of the circle, and the Point C is the center of the circle.
Assuming that line EH is also a straight line, using the vertical angles are always congruent theorem, m∠ECD = m∠HCG.
Therefore, m∠HCG = 45°
We always measure arcs in a counterclockwise direction.
⇒ m∡DF = m∡DE + m∡EF
= 45° + 60°
= 105°
