The above rectangle is divided into 3 congruent squares. The angles A, B and C are defined by the sides of the rectangle and the red segments.
A+B+C=X
Find X
(Answer is in degrees, does not require °)
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See figure. Construct 2 squares, EHGF and EIJF. We know that A=45 degrees. We let HJG=e degrees. and we also know that e+C=45 degrees= A We know that OH/OB=GH/GJ=1/2, thus angle B = angle e. Therefore, B=e and we can conclude that C+e=C+B=45 degrees, and A+B+C=90 degrees.