SOLUTION: if ray ACFG and ray BCDE intersect at C and angle ADC is conngruent to angle BFC, then angle ADE is congruent to angle BFG.

Algebra ->  Geometry-proofs -> SOLUTION: if ray ACFG and ray BCDE intersect at C and angle ADC is conngruent to angle BFC, then angle ADE is congruent to angle BFG.       Log On


   

Question 512636: if ray ACFG and ray BCDE intersect at C and angle ADC is conngruent to angle BFC, then angle ADE is congruent to angle BFG.
Answer by solver91311(24713) About Me  (Show Source):
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ADC and ADE are a linear pair and are therefore supplementary (the sum of their measures is 180). Same relationship for BFC and BFG.

So mADC + mADE = 180

mBFC + mBFG = 180

Hence mADC + mADE = mBFC + mBFG

But we are given that mADC = mBFC, so substitute:

mBFC + mADE = mBFC + mBFG

Subtract mBFC from both sides

mADE = mBFG : Q.E.D.

John

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