Question 362410
{{{drawing(300,300,-10,10,-10,10,circle(0,0,5),circle(0,5,0.3),circle(0,-5,0.3),circle(9.5,0,0.3),green(line(0,5,0,-5)),
green(line(0,0,4,3)),
green(line(0,0,4,-3)),
circle(4,3,0.3),
circle(4,-3,0.3),
locate(0.2,2,40),
locate(0.2,-1,40),
locate(1.5,0.5,A),
blue(line(0,5,9.5,0)),blue(line(0,-5,9.5,0)))}}}
The measure of all of the green segments is equal to the radius of the circle. 
Since the green legs are equal, both green-green-blue triangles are also isoceles with angles 70-70-40.
From the diagram,
{{{40+40+A=180}}}
{{{highlight(A=100)}}}degrees