Answer:
see explanation
Step-by-step explanation:
(a)
The angle on the circumference is half the central angle , that is
∠ A = ∠ BOC ÷ 2 = 50° ÷ 2 = 25°
(b)
Δ AOC is isosceles ( OA = OC , radii of the same circle ) then the base angles are congruent , that is
∠ ACO = ∠ A = 25°
(c)
Δ BOC is isosceles ( OB = OC, radii of the same circle ) then the base angles are congruent, that is
∠ BCO = [tex]\frac{180-50}{2}[/tex] = [tex]\frac{130}{2}[/tex] = 65°
(d)
∠ ACO + ∠ BCO = 25° + 65° = 90° ( angle in a semicircle )
