OU is the bisector of ∠U, and OV is the bisector of ∠V

Note that OV and OU form 2 sides of the triangle, OVU 



Let ∠SVO be x

Then ∠OVU also = x



Likewise, let ∠TUO be y

Then ∠OUV also = y



Since the interior angles of a quadrilateral sum to , we get:

2x + 2y + 60 + 80 = 360

2x + 2y + 140 = 360

2x + 2y = 220____2(x + y) = 2(110)_____x + y = 110

Since x and y are the 2 base angles of triangle, OVU, it follows that ∠UOV = 180 - (x + y), or 180 - 110 =  

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