Answer:
89.0°
Step-by-step explanation:
The measure of arc CD is the same degree measure as the central angle.
To find the central angle use the right triangle.
The segment from the centre to the chord is a perpendicular bisector, thus
the third side of the triangle = 12.7 ÷ 2 = 6.35
Calculate one half of the central angle using the sine ratio and multiply by 2 for the whole central angle
sin( one- half ) =[tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{6.35}{9.06}[/tex], hence
central angle = 2 × [tex]sin^{-1}[/tex] ([tex]\frac{6.35}{9.06}[/tex] ) ≈ 89.0°
Hence measure of CD ≈ 89.0°
