Question

What is the sum of the measures of the interior angles of a regular polygon where a single exterior angle measures 72°?

Answer 1

Recall that the exterior angles of a regular polygon add up to 360. So do the following:
\[n = \frac{360}{m\angle Exterior \space Angle}\]Then plug it into this formula.
\[Sum \space of \space interior \space angles = (n - 2)180\]

Answer 2

the exterior angles of a polygon sum to 360

the number of sides(angles) can be found by dividing 360 by the exterior angle

360/72 = 5

the polygon has 5 sides

the to find the angle sum can be found using

\[(n - 2)\times 180\]

Answer 3

thank you to both @campbell_st and @Calcmathlete :D

Answer 4

np :)