SOLUTION: If m∠BEC = 5x-25 and m∠DEA = 7x-65, find m∠BEC, m∠DEA, m∠DEB, and m∠AEC

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Question 796444: If m∠BEC = 5x-25 and m∠DEA = 7x-65, find m∠BEC, m∠DEA, m∠DEB, and m∠AEC
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
If m∠BEC = 5x-25 and m∠DEA = 7x-65, find m∠BEC, m∠DEA, m∠DEB, and m∠AEC


 ∠BEC and ∠DEA are vertical angles, so
they are congruent and their measures are equal

   5x-25 = 7x-65
     -2x = -40
       x = 20°

So m∠BEC = 5x-25 = 5(20)-25 = 100-25 = 75°

and m∠DEA = 7x-65 = 7(20)-65 = 140-65 = 75°


∠BEC and ∠DEB form a linear pair so the sum
of their measures is 180°, so m∠DEB = 180°-75° = 105°

∠AEC and ∠DEB are vertical angles, so they are
cngruent and their measures are equal, so m∠DEB = 105°

Edwin
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