Question

find x in the equation and assume that any segment that appears to be tangent is a tangent
theta=x small=45

Answer 1

small=45 --> I don't know what you mean by this.
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The formula:the angle formed by the intersection of 2 tangents outside the circle equals half the difference of the intercepted arcs.

34 = (1/2) [ (360 -x) - x]
68 = 360 - 2x
x = 146

Answer 2

Thank you