Question

Circle G contains the diameter BC
Find the measure of x and y.

Answer 1

x = 24°, y = 53°

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 =
`(1)/(2)` × 98° = 49°

Then

y + 78° + 49° = 180° (sum of angles in triangle )

y + 127° = 180° ( subtract 127° from both sides )

y = 53°