Answer:
∠ CAD = 30°
Step-by-step explanation:
The central angle ADB is equal to the arc AB subtending it, thus
∠ ADB = 60°, then
∠ ADC = 180° - 60° = 120° ( straight angle )
Since BC is a diameter then DC is a radius and AD = DC, thus
Δ ADC is isosceles with ∠ DCA = ∠ DAC
The sum of the 3 angles in a triangle = 180°, hence
∠ CAD = [tex]\frac{180-120}{2}[/tex] = [tex]\frac{60}{2}[/tex] = 30°
