Question 1204914
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<img src = "https://i.ibb.co/jfjvmnG/2023-11-13-22-24-08-Cerebral-Contortions-05-pdf-Brave.png">
Focus on triangle BCE. Use a pen or marker to make this highlight.
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Triangle BCE is a right triangle with these angles<ul><li>B = unknown</li><li>C = 90</li><li>E = 63</li></ul>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<ul><li>B = 27 (we just calculated)</li><li>F = unknown</li><li>D = 90</li></ul>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.



Answer: angle BFD = <font color=red size=4>63 degrees</font>
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