Question

calculate the sum of the interior angle measures of each polygon.
25 a polygon has 8 sides.
180(n - 2)° = 180(8 - 2)°
= 180(6)°
= 1080°
26 a polygon has 9 sides.
27 a polygon has 13 sides.
28 a polygon has 16 sides.
29 a polygon has 20 sides.
30 a polygon has 25 sides.

Explanation:

Problem 26: A polygon has 9 sides.

Step1: Identify the formula

The formula for the sum of interior angles of a polygon is \(180(n - 2)^\circ\), where \(n\) is the number of sides.

Step2: Substitute \(n = 9\)

Substitute \(n = 9\) into the formula: \(180(9 - 2)^\circ\)

Step3: Simplify the expression

First, calculate \(9 - 2 = 7\), then \(180\times7 = 1260\). So the sum is \(1260^\circ\).

Step1: Use the polygon angle formula

The formula is \(180(n - 2)^\circ\), with \(n = 13\).

Step2: Substitute \(n = 13\)

Substitute \(n = 13\) into the formula: \(180(13 - 2)^\circ\)

Step3: Calculate the result

\(13 - 2 = 11\), then \(180\times11 = 1980\). So the sum is \(1980^\circ\).

Step1: Recall the formula

The formula for the sum of interior angles is \(180(n - 2)^\circ\), where \(n = 16\).

Step2: Substitute \(n = 16\)

Substitute \(n = 16\) into the formula: \(180(16 - 2)^\circ\)

Step3: Simplify

\(16 - 2 = 14\), and \(180\times14 = 2520\). So the sum is \(2520^\circ\).

Answer:

\(1260^\circ\)

Problem 27: A polygon has 13 sides.