Question 1164931
<pre>
I won't do your for you.  I'll do one exactly like it.
</pre>ABCD is rhombus. If ∠BAC = 36°, find ∠ADB and ∠ ABC.<pre>
{{{drawing(400,400,-1,1,-1,1,

line(-cos(54*pi/180),0,0,sin(54*pi/180)),
line(cos(54*pi/180),0,0,sin(54*pi/180)),
line(-cos(54*pi/180),0,0,-sin(54*pi/180)),
line(cos(54*pi/180),0,0,-sin(54*pi/180)),
red(arc(0,sin(54*pi/180),.8,-.8,234,270)),
green(line(0,sin(54*pi/180),0,-sin(54*pi/180)),
line(-cos(54*pi/180),0,cos(54*pi/180),0)),
locate(-.02,.9,A),locate(-.65,.03,B),locate(.6,.03,D),
locate(-.02,-.81,C), locate(-.14,.65,36^o),
locate(0.02,0,E),
locate(.3,.15,"????"^o),locate(-.5,0.07,"????"^o),

red(arc(cos(54*pi/180),0,.8,-.8,126,180)),

red(arc(-cos(54*pi/180),0,.8,-.8,306,414))

 )}}}

∠ DAC = 36°   because the diagonals of a rhombus bisect each other.
AC ⊥ BC       because the diagonals of a rhombus are perpendicular.
ΔAED is a right triangle because two sides are perpendicular.
∠ ADB = 54°   because the two angles of a right triangle are complementary.

AB ≅ AD       Sides of a rhombus are congruent
ΔABD is isosceles   2 sides congruent
∠ ABD = 54°   Base angles of isosceles triangle are congruent
AB ≅ BC       Sides of a rhombus are congruent
ΔABC is isosceles   2 sides congruent
∠ BCA = 36°   Base angles of isosceles triangle are congruent
∠BAC + ∠BCA + ∠ABC = 180°    Property of all triangles
∠ABC = 180° - ∠BAC - ∠BCA  
∠ABC = 180° - 36° - 36° = 108°

Now do yours the same way.

Edwin</pre>