Answer:
Arc BC is 64°
Step-by-step explanation:
The parameters given are;
∠CAB = 32°
We note that the measure of arc BC = ∠CDB
∠DCA = ∠CAB = 32° (Base angles of an isosceles triangle)
∠ACB = 90° (Angle subtended at the center = Twice angle subtended at the circumference)
∠ACB = ∠DCB + ∠DCA
∴ ∠DCB = ∠ACB - ∠DCA = 90° - 32° = 58°
∠DBC = ∠DCB = 58° (Base angles of an isosceles triangle)
∴ ∠CDB + ∠DBC + ∠DCB = 180° (Sum of interior angles of a triangle)
∠CDB = 180° - (∠DBC + ∠DCB) = 180° - (58° + 58°) = 64°
∠CDB = Arc BC = 64°
