Answer:
x = 24°, y = 53°
Step-by-step explanation:
An inscribed angle is half the measure of its intercepted arc.
arc EC = 2 × ∠ EDC = 2 × 78° = 156°
x = arc BE = 180° - arc EC = 180° - 156° = 24°
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arc CD = 2 × CED = 2 × 41° = 82°
arc BD = 180° - arc CD = 180° - 82° = 98° , then
∠ BCD = [tex]\frac{1}{2}[/tex] × 98° = 49°
Then
y + 78° + 49° = 180° (sum of angles in triangle )
y + 127° = 180° ( subtract 127° from both sides )
y = 53°
