# Chapter 6 - Polygons and Quadrilaterals - 6-2 Properties of Parallelograms - Practice and Problem-Solving Exercises - Page 366: 52

$m$ of the interior angles in a $40$-gon = $6840^{\circ}$

#### Work Step by Step

According to the Polygon Angle-Sum Theorem, the sum of all the measures of the interior angles of a polygon is $(n - 2)180$, where $n$ is the number of sides of the polygon. We have a polygon that has $40$ sides. $m$ of the interior angles in a $40$-gon = $(40 - 2)180$ Evaluate what is in parentheses first, according to order of operations: $m$ of the interior angles in a $40$-gon = $(38)180$ Multiply to solve: $m$ of the interior angles in a $40$-gon = $6840^{\circ}$

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