Answer:
[tex]arc\ DC=30^o[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
The point P is the center of the circle (the drawing is not a scale )
step 1
Find the measure of angle ∠CPD
we know that
[tex]m\angle CPD+150^o=180^o[/tex] ---> by supplementary angles (form a linear pair)
[tex]m\angle CPD=180^o-150^o=30^o[/tex]
step 2
Find the measure of arc DC
we know that
Central angle is the angle that has its vertex in the center of the circumference and the sides are radii of it
so
[tex]arc\ DC=m\angle CPD[/tex] ----> by central angle
therefore
[tex]arc\ DC=30^o[/tex]