The sum of the measures of the interior angles of a convex polygon is 900^\circ. How many … — ACT

The sum of the measures of the interior angles of a convex polygon is $900^\circ$ . How many sides does this polygon have?

The polygon has 7 sides.

The correct answer is

7

because the sum of the interior angles of a convex polygon with

n

sides is

(n - 2) \times 180^\circ

. Setting this equal to

900^\circ

yields

(n - 2) \times 180 = 900

. Dividing both sides by

180

gives

n - 2 = 5

, and adding

2

to both sides results in

n = 7

Set up the equation for the sum of the interior angles of a polygon.

(n - 2) \times 180^\circ = 900^\circ

The sum of the interior angles of a convex polygon with

n

sides is always

(n - 2) \times 180^\circ

Divide both sides of the equation by

180^\circ

n - 2 = 5

To isolate the term with

n

, we divide

900

180

Solve for

n

by adding

2

to both sides.

n = 7

Adding

2

to both sides isolates the variable

n

The sum of the interior angles of an

n

-sided convex polygon is

(n - 2) \times 180^\circ

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