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
<pre>OU is the bisector of &#8736U, and OV is the bisector of &#8736V
Note that OV and OU form 2 sides of the triangle, OVU 

Let &#8736SVO be x
Then &#8736OVU also = x

Likewise, let &#8736TUO be y
Then &#8736OUV also = y

Since the interior angles of a quadrilateral sum to {{{360^o}}}, 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 &#8736UOV = 180 - (x + y), or 180 - 110 = {{{highlight_green(70^o)}}}