Question

self-assessment

1. the sum of the measures of the interior angles of a convex polygon is 1440°. classify the polygon by the number of sides.

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon

The formula for the sum of the interior angles of a convex polygon with \( n \) sides is \( S=(n - 2)\times180^{\circ} \), where \( S \) is the sum of the interior angles.

Step2: Substitute the given sum into the formula and solve for \( n \)

We know that \( S = 1440^{\circ} \). Substituting into the formula:
\[
1440=(n - 2)\times180
\]
First, divide both sides of the equation by \( 180 \):
\[
\frac{1440}{180}=n - 2
\]
Simplify the left - hand side: \( 8=n - 2 \)

Then, add 2 to both sides of the equation to solve for \( n \):
\[
n=8 + 2=10
\]

Answer:

The polygon is a decagon (a 10 - sided polygon).