SOLUTION: in a quadrilateral STUV the bisectors of angle U and angle V meet at a point O. if angle T=80 and angle S=60. find angle UOV

Algebra ->  Angles -> SOLUTION: in a quadrilateral STUV the bisectors of angle U and angle V meet at a point O. if angle T=80 and angle S=60. find angle UOV       Log On


   

Question 1062119: in a quadrilateral STUV the bisectors of angle U and angle V meet at a point O. if angle T=80 and angle S=60. find angle UOV

Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52786) About Me  (Show Source):
Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
in a quadrilateral STUV the bisectors of angle U and angle V meet at a point O. if angle T=80 and angle S=60. find angle UOV
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 360%5Eo, 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 = highlight_green%2870%5Eo%29