Answer:
∠U = 65°
Explanation:
You want the measure of external angle U formed by two tangents that intersect a circle creating major arc TV of 245°.
External angle
The measure of the external angle is half the difference of the two arcs of the circle that the secants (tangents) intercept.
The major arc is shown as 245°. The minor arc TV completes the circle, so is 360° -245°.
Half the difference is ...
(245° -(360°-245°))/2 = 245° -180° = 65°
Angle U is 65°.
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Additional comment
You will notice the angle formed by the tangents is 180° less than the measure of the major arc. (It is also equal to the supplement of the minor arc.)
A tangent is a special case of a secant, where the two points of intersection with the circle merge to a single point. The relations applicable to secants also apply to tangents.