Answer:
u = 24, v = 92, and w = 184
Explanation:
According to circle theorem, we have;
∠ACD = ∠ABD = 88° by angle inscribed in a circle and also subtending the same chord
∠DOA = 2 × ∠ABD by angle subtended at the center = 2 × Angle subtended at the circumference
∴ ∠DOA = 2 × ∠ABD = 2 × 88° = 176°
w° + ∠DOA = 360 by the sum of angles at a point
∴ w° = 360° - ∠DOA = 360° - 176° = 184°
w° = 184°
w° = 2 × v° by angle subtended at the center = 2 × Angle subtended at the circumference
∴ v° = w°/2 = 184°/2 = 92°
v° = 92°
In triangle ΔCDY and ΔABY, we have;
∠ABD = ∠ABY by reflexive property
∠ACD = ∠ACY by reflexive property
∠ACD = ∠ABD = 88°
∴ ∠ABY = 88°
∠CYD = ∠AYB by vertically opposite angles are equal
∴ ∠CYD = 68° = ∠AYB
u° + ∠ABY + ∠AYB = 180° by angle sum property
∴ u° = 180° - (∠ABY + ∠AYB)
u° = 180° - (88° + 68°) = 24°
u° = 24°.