Answer:
? = 50°
Explanation:
You want the measure of the angle between tangents, when the major arc they intercept is 230°.
Angle relations
The exterior angle (?) is half the difference of the two arcs it intercepts. Here, the two arcs form a circle, so we have ...
? = 1/2(230° -(360° -230°)) = 1/2(2·230° -360°)
? = 230° -180° = 50°
The angle at C is 50°.
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Additional comment
The external angle between tangents at C can also be found as the supplement of the central angle BOD if the center of the circle is point O.
The above relation (half the difference of intercepted arcs) is true for secants as well as tangents.