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Focus on triangle BCE. Use a pen or marker to make this highlight.
Or you can use your favorite paint program to help you focus on this triangle.
Triangle BCE is a right triangle with these angles
B = unknown
C = 90
E = 63
Use the fact that all 3 interior angles of a triangle add to 180 degrees.
B+C+E = 180 leads to B+90+63 = 180 which solves to B = 180-90-63 = 27
Therefore, angle EBC = 27
Now turn your attention to triangle BFD. It is also a right triangle with these angles
B = 27 (we just calculated)
F = unknown
D = 90
B+F+D = 180 leads to 27+F+90 = 180 and solves to F = 63 and therefore angle BFD = 63.
Side note: it turns out that triangle BCE is similar to triangle BDF. Use the angle angle (AA) similarity theorem to prove this claim.
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