Answer:
The measure of arc CD is [tex]114.6\°[/tex]
Step-by-step explanation:
see the attached figure with letters to better understand the problem
we know that
The measure of arc CD is equal to the angle CAD by central angle
The measure of angle CAD is equal to the angle CAB multiplied by 2
Find the measure of angle CAB
In the right triangle ABC
[tex]sin(CAB)=\frac{BC}{AC}[/tex]
[tex]BC=BD=36.7/2=18.35\ in[/tex]
substitute the values
[tex]sin(CAB)=\frac{18.35}{21.8}[/tex]
[tex]< CAB=arcsin(\frac{18.35}{21.8})=57.32\°[/tex]
Find the measure of angle CAD
[tex]m<CAD=2*m<CAB[/tex]
[tex]m<CAD=2*(57.32\°)=114.6\°[/tex]
therefore
The measure of arc CD is [tex]114.6\°[/tex]
