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63o.

Join the points where the tangents touch the circle to its centre to form a quadrilateral (two meeting tangents and two radii).

These angles are both 90o, summing to 180o.

Thus the other two angles - the one at the centre of the circle and the one where the tangents meet - sum to 360o - 180o = 180o (they are supplementary).

The centre angle is given as 117o (the minor arc), so the angle where the tangents met is 180o - 117o = 63o.

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Q: What is the measure of the angle formed by two tangents drawn to a circle from an external point if they intersect a major arc whose measure is 243 and the minor arc measures 117?
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