Question 1195065: In ∆ABC in the diagram below, D and E are points on side AB, and F and G are points on side AC, such that AD = DG = GB = BC = CE = EF = FA. Find ∠BAC.
Found 2 solutions by lotusjayden, greenestamps:
Answer by lotusjayden(18)   (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Use the diagram posted by the other tutor (copy it to paper so you can follow the discussion below).
Let m(BCA) = x. Since AD=DG, m(AGD) = x.
Then m(ADG) = 180-2x; so m(BDG) = 2x.
Since DG=GB, m(DBG) = 2x; so m(BGD) = 180-4x.
Then, with m(AGD) = x and m(BGD) = 180-4x, m(BGC) = 3x.
Since GB = BC, m(GCB) = 3x; and that makes m(CBG) = 180-6x.
With m(DBG) = 2x and m(CBG) = 180-6x, m(CBD) = 180-4x; then since BC = CE, m(BEC) = 180-4x; that then makes m(BCE) = 8x-180.
With m(GCB) = 3x and m(BCE) = 8x-180, m(ECG) = 180-5x.
Then CE = EF means m(CFE) = 180-5x; and then m(CEF) =10x-180.
With m(BEC) = 180-4x and m(CEF) = 10x-180, m(FEA) = 180 - 6x.
Finally, EF = FA means m(BCA) = m(FEA): x = 180-6x.
Solving for x....
x = 180-6x
7x = 180
x = 180/7
ANSWER: The measure of angle BAC is x = 180/7 degrees
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