```Question 331516
{{{drawing(400,400,-.8,1.2,-.5,1.5,

line(0,0,2*cos(80*pi/180),0),
line(0,0,cos(80*pi/180),sin(80*pi/180)),

line(2*cos(80*pi/180),0,cos(80*pi/180),sin(80*pi/180)),

line(cos(80*pi/180),sin(80*pi/180),.6736481777,.5652579374),

line(.6736481777,.5652579374,2*cos(80*pi/180),0),

locate(0,0,B), locate(.17,1.05,A), locate(.35,0,C),locate(.7,.6,D) )}}}

<pre><font size = 4 color = "indigo"><b>

Locate point E so that triangle EAB is congruent to triangle DAC

{{{drawing(400,400,-.8,1.2,-.5,1.5,

line(0,0,2*cos(80*pi/180),0),
line(0,0,cos(80*pi/180),sin(80*pi/180)),

line(2*cos(80*pi/180),0,cos(80*pi/180),sin(80*pi/180)),

line(cos(80*pi/180),sin(80*pi/180),.6736481777,.5652579374),

line(.6736481777,.5652579374,2*cos(80*pi/180),0),

locate(0,0,B), locate(.17,1.05,A), locate(.35,0,C),locate(.7,.6,D),

green(line(0,0,-.3263518224,.5652579374), line(-.3263518224,.5652579374,

cos(80*pi/180),sin(80*pi/180)),locate(-.4,.6,E))

)}}}

Draw ED

{{{drawing(400,400,-.8,1.2,-.5,1.5,

line(0,0,2*cos(80*pi/180),0),
line(0,0,cos(80*pi/180),sin(80*pi/180)),

line(2*cos(80*pi/180),0,cos(80*pi/180),sin(80*pi/180)),

line(cos(80*pi/180),sin(80*pi/180),.6736481777,.5652579374),

line(.6736481777,.5652579374,2*cos(80*pi/180),0),

locate(0,0,B), locate(.17,1.05,A), locate(.35,0,C),locate(.7,.6,D),

green(line(0,0,-.3263518224,.5652579374), line(-.3263518224,.5652579374,

cos(80*pi/180),sin(80*pi/180)),locate(-.4,.6,E)),

red(line(-.3263518224,.5652579374,.6736481777,.5652579374))
)}}}
Extend BC to F so that CF = CD.  Draw DF
{{{drawing(400,400,-.8,1.2,-.5,1.5,

line(0,0,2*cos(80*pi/180),0),
line(0,0,cos(80*pi/180),sin(80*pi/180)),

line(2*cos(80*pi/180),0,cos(80*pi/180),sin(80*pi/180)),

line(cos(80*pi/180),sin(80*pi/180),.6736481777,.5652579374),

line(.6736481777,.5652579374,2*cos(80*pi/180),0),

locate(0,0,B), locate(.17,1.05,A), locate(.35,0,C),locate(.7,.6,D),

green(line(0,0,-.3263518224,.5652579374), line(-.3263518224,.5652579374,

cos(80*pi/180),sin(80*pi/180)),locate(-.4,.6,E)),

red(line(-.3263518224,.5652579374,.6736481777,.5652579374)),

green(line(2*cos(80*pi/180),0,1,0),line(.6736481777,.5652579374,1,0),
locate(1,0,F))

)}}}

I won't go through every step.  I'll just tell you enough so
you can write it out like your teacher wants you to.

Using the fact that isosceles triangles have equal
base angles, that interior angles of a triangle have sum 180°,
that supplementary angles have sum 180°, and that vertical angles
are equal,  you can now write the number of degrees in every
angle in the figure.  That would be a good idea.

Therefore it is easy to show that