Ihave to find the length of the angle indicated for the trapezoid

That is not a trapezoid, it is a general quadrilateral.  All 2-dimensional, 4-sided figures have an internal angle sum of 360 (triangles are 180).  So if you assume angles P and Q are right, they are each equal to 90 degrees, for a total of 180.
Subtract: 360 - 180 = 180.  We know that S + R must equal 180.  If you subtract 180 - 65, you get 115, which is obtuse (greater than 90 degrees).  This matches the drawing as the unknown angle is clearly greater than 90.  So the answer is 115 degrees.