Question 1100967
The question should state
"In a regular polygon each interior angle is 150 degrees greater than each exterior angle".
An exterior angle is the change of direction needed at each vertex to go around the polygon.
It is supplementary to the adjacent interior angle,
meaning that both of them add up to {{{180^o}}} .
For example, here is a regular hexagon, with an interior angle and an exterior angle labeled as such:
{{{drawing(300,300,-2.2,2.2,-2.2,2.2,
line(-1,-1.732,1,-1.732),line(-1,1.732,1,1.732),
line(-1,-1.732,-2,0),line(-2,0,-1,1.732),
line(2,0,1,-1.732),line(2,0,1,1.732),
arrow(1,-1.732,2.2,-1.732), red(arc(1,-1.732,1,1,-60,0)),
green(arc(1,-1.732,2,2,180,300)),
locate(0.2,-1.2,green(interior)),locate(0.2,-1.4,green(angle)),
locate(1.4,-1.2,red(exterior)),locate(1.5,-1.4,red(angle))
)}}}
 
In a regular polygon,
if each interior angle is 150 degrees greater than each exterior angle,
all exterior angles measure {{{x}}} degrees,
and all interior angles measure {{{150+x}}} degrees,
{{{150+2x=180}}} , {{{2x=30}}} and {{{x=15}}}.
If you change direction by {{{15}}} degrees at each vertex,
one whole turn going around the polygon, adding up a {{{360^o}}} turn,
will require {{{360/15=24}}} changes of direction at {{{24}}} vertices,
and the polygon has {{{highlight(24)}}} sides.
 
The teacher wants you to remember that the sum of the interior angles of a polygon with {{{n}}} sides is {{{(n-2)*180^o}}} ,
but without remembering,
you would intuitively know that for all polygons,
the sum of all exterior angles is {{{360^o}}} ,
and it makes calculations faster/easier in this case.