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A quadrilateral has angles of $q$, $4q + 17^\circ $, $8q + 21^\circ$, and $15q + 148^\circ $. Find the largest angle of the quadrilateral, in degrees.

 Jan 23, 2025
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A quadrilateral has angles of $q$, $4q + 17^\circ $, $8q + 21^\circ$, and $15q + 148^\circ $. Find the largest angle of the quadrilateral, in degrees.    

 

q  +  (4q + 17o)  +  (8q + 21o)  +  (15q + 148o)  =  360o    

 

28q + 186o  =  360o    

 

28q  =  174o    

 

q  =  174o / 28  =  6.2o     rounded to 6.2 here, but I didn't round it in my calculator    

 

by observation it's obvious that the largest angle is (15q + 148o)    

 

(15 6.2o) + 148o  =  241.2o    

.    

 Jan 23, 2025

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