Question 796444
If m∠BEC = 5x-25 and m∠DEA = 7x-65, find m∠BEC, m∠DEA, m∠DEB, and m∠AEC
<pre>
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locate(-.608761429,-.7933533403,C),
locate(.608761429,-.7933533403,B),
locate(-.608761429,.85,A),
locate(.608761429,.85,D),
locate(.05,.05,E),
locate(-.125,.3,7x-65), locate(-.125,-.2,5x-25),
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 &#8736;BEC and &#8736;DEA are vertical angles, so
they are congruent and their measures are equal

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

So m&#8736;BEC = 5x-25 = 5(20)-25 = 100-25 = 75°

and m&#8736;DEA = 7x-65 = 7(20)-65 = 140-65 = 75°


&#8736;BEC and &#8736;DEB form a linear pair so the sum
of their measures is 180°, so m&#8736;DEB = 180°-75° = 105°

&#8736;AEC and &#8736;DEB are vertical angles, so they are
cngruent and their measures are equal, so m&#8736;DEB = 105°

Edwin</pre>