SOLUTION: Find &#8736;<font face="symbol">q</font> Find &#8736;<font face="symbol">f</font> {{{drawing(400,52400/233,-10,223,-10,121, locate(100,0,AB=213), locate(214,56,111), line(0,0,2

Algebra ->  Triangles -> SOLUTION: Find &#8736;<font face="symbol">q</font> Find &#8736;<font face="symbol">f</font> {{{drawing(400,52400/233,-10,223,-10,121, locate(100,0,AB=213), locate(214,56,111), line(0,0,2      Log On


   



Question 1036184: Find ∠q
Find ∠f

Found 2 solutions by Edwin McCravy, MathTherapy:
Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!

This figure is drawn to scale:


AE = AB-EB = AB-DC = 213-185 = 28

tan(∠DAE) = %22opposite%22%2F%22adjacent%22 = DE%2F%22AE%22 = CB%2F%22AE%22 = 111%2F28

∠DAE = 75.84236735°

tan(∠CAB) = %22opposite%22%2F%22adjacent%22 = CB%2FAB = 111%2F213

∠CAB = 27.52522574°

∠q = ∠DAE-∠CAB = 75.84236735°-27.52522574° = 48.31714161°

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∠f is an exterior angle to ΔAEF,
so it is the sum of the two remote interior angles of ΔAEF,

so ∠f = ∠CAE + ∠AEF = 27.52522574°+ 90° = 117.5252257°

Edwin

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

q = ∠DAE - ∠CAE = 75.84 – 27.53, or highlight_green%2848.31%5Eo%29
f = ∠CAE + ∠AEF, or 27.53 + 90, or highlight_green%28117.53%5Eo%29