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 + 17) + (8q + 21) + (14q + 148) = 360
27q + 186 = 360
27q = 174
q = 174 / 27 = 58 / 9
Largest angle = 14 (58 / 9) + 148 ≈ 238.22°
+1418 
