Question 1209450
<font color=black size=3>
This is what the diagram could look like if you follow the steps tutor greenestamps wrote
{{{
drawing(400,400,-4,4,-3.5,4.5,

line(0.02,3.02,-1.62,-2),line(-1.62,-2,1.64389,-2.00523),line(1.64389,-2.00523,0.02,3.02),line(1.64389,-2.00523,-0.99358,-0.08253),

circle(0.02,3.02,0.06),circle(0.02,3.02,0.08),circle(0.02,3.02,0.1),circle(0.02,3.02,0.12),circle(-1.62,-2,0.06),circle(-1.62,-2,0.08),circle(-1.62,-2,0.1),circle(-1.62,-2,0.12),circle(1.64389,-2.00523,0.06),circle(1.64389,-2.00523,0.08),circle(1.64389,-2.00523,0.1),circle(1.64389,-2.00523,0.12),circle(-0.99358,-0.08253,0.06),circle(-0.99358,-0.08253,0.08),circle(-0.99358,-0.08253,0.1),circle(-0.99358,-0.08253,0.12),

locate(-0.1,1.9,2x),locate(0.64,-0.74,2x),locate(0.44-0.2,-1.62,90-3x),locate(-1.2,-1.66,90-x),locate(-0.88,-0.64,90-x),

locate(0.22,3.12,"A"),locate(-1.72,-2.2,"B"),locate(1.84389,-2.20523,"C"),locate(-0.79358-0.6,-0.28253+0.6,"D")

)
}}}


From there focus on isosceles triangle BCD to set up the equation
B+C+D = 180
(90-x)+(90-3x)+(90-x) = 180
That equation solves to x = 18, so 2x = 2*18 = <font color=red>36 degrees</font> is the measure of angle A.


--------------------------------------------------------------------------


If you prefer tutor ikleyn's approach, then the diagram could look like this

{{{
drawing(400,400,-4,4,-3.5,4.5,

line(0.02,3.02,-1.62,-2),line(-1.62,-2,1.64389,-2.00523),line(1.64389,-2.00523,0.02,3.02),line(1.64389,-2.00523,-0.99358,-0.08253),

circle(0.02,3.02,0.06),circle(0.02,3.02,0.08),circle(0.02,3.02,0.1),circle(0.02,3.02,0.12),circle(-1.62,-2,0.06),circle(-1.62,-2,0.08),circle(-1.62,-2,0.1),circle(-1.62,-2,0.12),circle(1.64389,-2.00523,0.06),circle(1.64389,-2.00523,0.08),circle(1.64389,-2.00523,0.1),circle(1.64389,-2.00523,0.12),circle(-0.99358,-0.08253,0.06),circle(-0.99358,-0.08253,0.08),circle(-0.99358,-0.08253,0.1),circle(-0.99358,-0.08253,0.12),

locate(-0.1,1.9,x),locate(0.64,-0.74,x),locate(0.44-0.2,-1.62,y-x),locate(-1.2,-1.66+0.1,y),locate(-0.88,-0.64,y),locate(-0.88+0.2,-0.64+0.8,180-y),


locate(0.22,3.12,"A"),locate(-1.72,-2.2,"B"),locate(1.84389,-2.20523,"C"),locate(-0.79358-0.6,-0.28253+0.6,"D")

)
}}}
Triangle ABC gives the equation x+2y = 180
Triangle BCD gives the equation -x+3y = 180
Solving that system yields (x,y) = (<font color=red>36</font>, 72)


Which updates the diagram to
{{{
drawing(400,400,-4,4,-3.5,4.5,

line(0.02,3.02,-1.62,-2),line(-1.62,-2,1.64389,-2.00523),line(1.64389,-2.00523,0.02,3.02),line(1.64389,-2.00523,-0.99358,-0.08253),

circle(0.02,3.02,0.06),circle(0.02,3.02,0.08),circle(0.02,3.02,0.1),circle(0.02,3.02,0.12),circle(-1.62,-2,0.06),circle(-1.62,-2,0.08),circle(-1.62,-2,0.1),circle(-1.62,-2,0.12),circle(1.64389,-2.00523,0.06),circle(1.64389,-2.00523,0.08),circle(1.64389,-2.00523,0.1),circle(1.64389,-2.00523,0.12),circle(-0.99358,-0.08253,0.06),circle(-0.99358,-0.08253,0.08),circle(-0.99358,-0.08253,0.1),circle(-0.99358,-0.08253,0.12),

locate(-0.1-0.1,1.9,red(36^o)),locate(0.64,-0.74,36^o),locate(0.44-0.2,-1.62+0.2,36^o),locate(-1.2,-1.66+0.2,72^o),locate(-0.88,-0.64,72^o),locate(-0.88+0.2,-0.64+0.9,108^o),

locate(0.22,3.12,"A"),locate(-1.72,-2.2,"B"),locate(1.84389,-2.20523,"C"),locate(-0.79358-0.6,-0.28253+0.6,"D")

)
}}} 


Answer: <font color=red>36 degrees</font>


Edit: I just realized that ikleyn completely plagiarized her answer. Doesn't surprise me. 
</font>