Can someone help EDC is similar to ABC. Solve for x.

△EDC  is similar to  △ABC ,  so side  DC  corresponds to side  BC .

Let the scale factor from  △EDC  to  △ABC  be  s .

DC * s   =   BC

4 * s   =   6

s   =   6/4

s   =   1.5

So each side of  △ABC  is  1.5  times the corresponding side of  △EDC.

△EDC  is similar to  △ABC ,  so side  EC  corresponds to side  AC .

EC * 1.5   =   AC

And we can see from the picture that   EC  =  x   and   AC  =  12.5 - x  , so....

x * 1.5   =   12.5 - x

1.5x   =   12.5 - x

                                 Add  x  to both sides of the equation.

1.5x + x   =   12.5

2.5x   =   12.5

                                 Divide both sides by  2.5 .

x   =   5

The sum of the angles in every triangle is  180° , so..

∠A + ∠B + ∠C   =   180°

21° + 90° + ∠C   =   180°

∠C   =   180° - 21° - 90°

∠C   =  69°

∠D  corresponds to  ∠A  so...

∠D   =   ∠A   =   21°

∠F  corresponds to  ∠C  so...

∠F  =  ∠C  =  69°