22. Liza found the total of the interior angles of a convex polygon. She missed one of the angles and obtained the result $2017^{\circ}$. Which of the following was the angle she missed?
A $37^{\circ}$
B $53^{\circ}$
C $97^{\circ}$
D $127^{\circ}$
E $143^{\circ}$
22. E Let $x^{\circ}$ be the missing angle. The correct total of the angles is then $(2017+x)^{\circ}$. The interior sum of angles in a polygon with $n$ sides is $180(n-2)^{\circ}$, so we require $2017+x$ to be a multiple of 180 . The larger multiples of 180 are 2160 plus any multiple of 180 . Hence $x=143$ plus any multiple of 180 . However, the polygon is convex so $x=143$.