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Lines \($l$ and $k$\) are parallel to each other. \($m\angle A = 120^\circ$, and $m\angle C = 80^\circ$\). What is the number of degrees in \($m\angle B$\)?

 Mar 19, 2020
edited by Guest  Mar 19, 2020
 #1
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Note  that if we drew a perpedicular to both  l and k   we would have an (irregular) pentagon

 

Call the intersection points of this perpendicular  to l and  k , D and E, respectively

 

And since  l and k  are parallel then angle   ADE   = angle  BED   =  90°

 

And since the sum of the interior angles of a pentagon  = 540°

 

So

 

angle A + angle C + angle B + angle D + angle E  = 540

 

120   +  80  +  angle B + 90   +  90    = 540    simplify

 

380 + angle B =  540   subtract  380  from both sides

 

angle B  = 160°

 

 

cool cool cool

 Mar 19, 2020

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