Question

1. farm an animal pen is in the shape of a regular heptagon. what is the measure of each interior angle of the animal pen? round to the nearest tenth.

Explanation:

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

The sum of the interior angles of a polygon with \( n \) sides is given by \( S=(n - 2)\times180^{\circ} \). For a heptagon, \( n = 7 \).
So, \( S=(7 - 2)\times180^{\circ}=5\times180^{\circ} = 900^{\circ} \).

Step2: Find the measure of each interior angle of a regular heptagon

In a regular polygon, all interior angles are equal. So, each interior angle \( \theta=\frac{S}{n} \).
Substituting \( S = 900^{\circ} \) and \( n = 7 \), we get \( \theta=\frac{900^{\circ}}{7}\approx128.6^{\circ} \) (rounded to the nearest tenth).

Answer:

\( 128.6^{\circ} \)