SOLUTION: In the diagram, find the measure of ∠ BFD. https://ibb.co/xsSFXH4

Question 1208920: In the diagram, find the measure of ∠ BFD.
https://ibb.co/xsSFXH4
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.


Consider quadrilateral DECF.


As for any quadrilateral, the sum of its interior angles is 360°.


The angles D and C of this quadrilaterals are right angles;
their sum is  90° + 90° = 180°.


Hence, the sum of angles F and E of this quadrilateral is  360° - 180° = 180°.


Thus the angle CFD is the supplementary angle to angle E: ∠CFD = 180° - 57° = 123°.


But the angle BFD is the supplementary angle to the angle CFD.


So, we conclude that  ∠BFD = 180° - 123° = 57°.


ANSWER.  ∠BFD = 57°.

Solved.

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