Question 841266
<pre>
Since the measures of the two big angles are 4 times the
measure of each of the smaller angles, let's put x in the
smaller angles and 4x in the bigger angles before we even
draw the diagonals: 

{{{drawing(500/3,400,-.5,.5,-1.2,1.2,
locate(-.02,1.05,A),locate(-.02,-.96,C),
locate(-.39,.05,B),locate(.34,.05,D),
line(cos(2pi/5),0,0,sin(2pi/5)),
line(cos(2pi/5),0,0,-sin(2pi/5)),
line(-cos(2pi/5),0,0,sin(2pi/5)),
line(-cos(2pi/5),0,0,-sin(2pi/5)),
locate(-.02,.8,x),locate(-.02,-.7,x),
locate(-.29,.05,4x),locate(.19,.05,4x)


 )}}}{{{matrix(24,1,

The,sum,of,the,measures,of, the,four,angles,is,"360°",so,x+4x+x+4x="360°",10x="360°",x="36°",
so,"m<BAD"="36°",and,"m<ABC"="144°",Now,we, draw,the,diagonals


)}}}{{{drawing(500/3,400,-.5,.5,-1.2,1.2,
locate(-.02,1.05,A),locate(-.02,-.96,C),
locate(-.39,.05,B),locate(.34,.05,D),
line(cos(2pi/5),0,0,sin(2pi/5)),
line(cos(2pi/5),0,0,-sin(2pi/5)),
line(-cos(2pi/5),0,0,sin(2pi/5)),
line(-cos(2pi/5),0,0,-sin(2pi/5)),
locate(-.02,.8,x),locate(-.02,-.7,x),
locate(-.29,.05,4x),locate(.19,.05,4x),
green(line(-cos(2pi/5),0,cos(2pi/5),0),
line(0,-sin(2pi/5),0,sin(2pi/5))),locate(.02,0,E)


 )}}}{{{matrix(17,1,

The,diagonals,bisect,the, interior,angles,of,the,rhombus,so,"m<EBC",is,
half,of,"m<ABC"="144°",so,"m<EBC"="72°"


)}}}

Edwin</pre>