Question 882689
{{{drawing(300,300,-2,10,-2,10,grid(1),circle(5,7,0.2),
circle(4,3,0.2),circle(8,2,0.2),
line(5,7,4,3),
line(4,3,8,2),
line(8,2,5,7))}}}
Calculate the edge lengths,
{{{DE^2=(5-4)^2+(7-3)^2}}}
{{{DE^2=1+16}}}
{{{DE^2=17}}}
.
.
{{{DF^2=(5-8)^2+(7-2)^2}}}
{{{DF^2=9+25}}}
{{{DF^2=34}}}
.
.
{{{EF^2=(4-8)^2+(3-2)^2}}}
{{{EF^2=16+1}}}
{{{EF^2=17}}}
.
.
The triangle is an isosceles (two equal sides) and right triangle ({{{DE^2+EF^2=DF^2}}}).
So then the angles are 45-45-90. 
Angle DEF is 90.