Question

1. the sum of the measures of six angles of an heptagon is 845°. what is the measure of the seventh angle?

Explanation:

Step1: Recall the sum of interior angles of a heptagon.

The formula for the sum of the interior angles of a polygon is \((n - 2)\times180^{\circ}\), where \(n\) is the number of sides. For a heptagon, \(n = 7\). So the sum of interior angles is \((7 - 2)\times180^{\circ}=5\times180^{\circ} = 900^{\circ}\).

Step2: Calculate the seventh angle.

Let the measure of the seventh angle be \(x\). We know that the sum of six angles is \(845^{\circ}\) and the total sum of all seven angles is \(900^{\circ}\). So we have the equation \(845^{\circ}+x = 900^{\circ}\). Solving for \(x\), we get \(x=900^{\circ}- 845^{\circ}=55^{\circ}\).

Answer:

The measure of the seventh angle is \(55^{\circ}\).