Is my answer correct? :/?

Your answer is correct but your approach is not. The 3 interior angles in a triangle add up to 180 degrees. Because triangle CED is isosceles, angle E equals to angle C. And so 45+45+D=180 and D=90 degrees.

I prove the line DC must be 90 degs I dont assume it like others do ... this may be one of the things your teacher wishes you to do

you can use many rules for proving the angles ...

you are given angle E = 45

ANGLE D + ANGLE c + ANGLE e = 180

YOU can PROVE ANGLE c maybe by a few of the rules for angles

if D to E is a line on the X axis just to simplify ..

and we know D TO E = D TO C

a perpendicular line from E to level of C should be easy to draw

we can draw a 90 deg angle up from E to the llevel of C call this point B

point B is perpendicular to the DE line

and has the angle DEC has the same angle as BEC

since EC is the same length... that means DE and BE must be the same length

that means that CD must be perpendicular to the x axis too.. because it is parallel to the line BE

the angle then at D must be 90 degs

since a triangle has a sum = 180 = angle C + 90 + 45

C = 180 - 135 = 45

The sum of 3 internal angles of a triangle is 180° .

So ∠C + ∠D + ∠E = 180° .

△ABC is an isosceles triangle with DE = DC , so ∠E = ∠C .

∠E = 45° , so ∠C = 45° .

Therefore 45° + ∠D + 45° = 180° .

So ∠D = 90° .

Yes because angle D is 180 -45 -45 = 90 degrees

YES!!!

Since angle E = 45 degrees, then angle C = 45 degrees (Isosceles).

Hence by summation of the angles of a triangle 180 = D + 45 + 45 => 180 = D + 90

D = 180 - 90 => D = 90