Answer:
∠ C = 40° , x = y = 118
Explanation:
10
BC is the diameter of the circle then ∠ A = 90° , angle in a semicircle.
the sum of the 3 angles in Δ ABC = 180° , then
∠ A + ∠ B + ∠ C = 180°
90° + 50° + ∠ C = 180°
140° + ∠ C = 180° ( subtract 140° from both sides )
∠ C = 40°
11
ABCD is a cyclic quadrilateral
• the opposite angles are supplementary, sum to 180°
x + 62 = 180 ( subtract 62 from both sides )
x = 118
similarly
y + 62 = 180
y = 118
thus x = y = 118