if the sum of the exterior angles of a polygon is one-fifth of the sum of the interior angles of the polygon, how many sides does the polygon have?

As the measure of the exterior angles of a regular polygon are 15 times the measure of its interior angles, each exterior angle of the regular polygon too will be 15 times the measure of its interior angle. we have 360∘30∘=12 exterior or interior angles i.e. Polygon has 12 sides - it is dodecagon

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is