How many sides would there be in a convex polygon if the sum of all but one of its interior angles is $1070^{\circ}$?
There will be ten sides.
8 sides (octagon)
180(n-2)=1070+m where m<180 and (1070+m)mod180=0
n-2=(1070+m)/180
n-2=5+(170+m)/180
m=10
n-2=5+(170+10)/180
n-2=5+1
n-2=6
n=8
+184 
