10) Calculate angle u, v and w
A
Y
с
88
68

u = 24, v = 92, and w = 184

Step-by-step 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°.