Answer :
Examining the figure, the missing angles are
angle AOC = 148 degrees
angle OCD = 21 degrees
How to find the angles
Line AB and CB are tangents to the circle and hence will make angle 90 degrees at the point of tangent.
OA bisects angle AOC and angles ABC
In triangle AOB
90 + 32/2 + angle AOB = 180 degrees
angle AOB = 180 - 90 - 32 / 2
angle AOB = 74 degrees
angle AOC = 74 x 2 = 148 degrees
Using inscribed angle theorem
angle D = 1/2 x angle AOC
angle D = 74 degrees
In quadrilateral ABCD
143 + 32 + 74 + angle C = 360
angle C = 360 - 143 - 32 - 74
angle C = 111 degrees
angle OCD = 111 - 90
angle OCD = 21 degrees
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