Answer:
The measure of arc CD is 114.6°.
Step-by-step explanation:
Let the center of the circle be O and OP is perpendicular to CD at point point P.
The perpendicular line from the center of circle divide each chord in two equal parts. so, CP=DP.

In a right angles triangle,

In a right angles triangle OPC,



In triangle OPC and OPD,
(Radius)
(Reflexive property)
(Altitude on chord from center)
By SSS postulate

(CPCTC)

The measure of angle COD is




Therefore the measure of arc CD is 114.6°.