Find the angle,2x, in the wedge shown

The problem can be solved using the cosine rule,
where 
cos(A)=(b^2+c^2-a^2)/(2bc)
=(12.5^2+12.5^2-8^2)/(2*12.5*12.5)
=.7952
=> A=2x=37.33 deg. =>
x=18.66 deg.

HOWEVER, since the triangle is isosceles, we can divide it into two right triangles, with short leg=4", and hypotenuse 12.5",  and solve easily by
x=asin(4/12.5)=18.66 degrees

Step-by-step explanation:

Right triangle ABC is reflected over AC to form triangle AFC.

Triangle AFC dilated by a scale factor of two-thirds to form triangle DEC.

Reflection is a rigid transformation which preserves lengths and angles, then

Dilation is a transformation which maps the triangle into similar triangle, so

Thus,

Similar triangle have congruent corresponding angles, so

and proportional corresponding sides

Thus, correct options are: