join the centres of the two circles. note that the sides of this trapezoid are nothing but the direct common tangents of these two circles. you just have to find the angle of inclination of the DCT to the line joining the centres. its easy. then finding the base angles is straightforward.
the distance between the parallel sides is 3+3+1+1=8.
once you get the above said thing you can find the lengths of each of the parallel sides. can you finish?
try solving a separate question:
Two circles, one of radius 3 and the other of radius 1 are touching externally at a point. Draw the direct common tangents of these circles. what is the angle between these two direct common tangents??
First find the length of a common tangent.Two sides of a defining right triangle are available by drawing a few construction lines.Try this and see if you can go forward. Similar triangles are involved. If stuck repost.
Look at post 6.Extend the slant lines to meet at A. Bottom corners Band C.From centers draw perpendiculars to one common tangent meeting at the points of tangency.Draw a perpendicular from center r=1 to the radius 3.Formed is a rectangle height 1 and length common tangent and a rt triangle hyp 4 side 2.This gives you a ct of 2rad3.It also supplies info on triangle ABC.Carry on from there