Find the missing angle?

Geometry Level 2

A B C D ABCD is a rectangle with A B = 10 AB = 10 and A F = F B AF = FB as shown below. If the area of the △ F B C = 25 2 \triangle FBC = \dfrac{25}{\sqrt 2} , what is the measure of ∠ D E C \angle{DEC} in degrees?


The answer is 90.

Ossama Ismail by Ossama Ismail , 63, Egypt

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2 solutions

Edwin Gray
Jun 26, 2018

Assuming F is the mid-point of AB, the slope of FC is - sqrt(2). The slope of BD is 1/sqrt(2). The product of slopes = -1, so the lines are perpendicular and E = 90. Ed Gray

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X X
May 5, 2018

You should add A F = F B AF=FB

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