Question

the sum of the interior angles of an octagon is 1080°. each angle incre degrees. what is the measure of the sixth angle?
_____ degrees

Explanation:

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

The formula for the sum of interior angles of a polygon is \((n - 2)\times180^{\circ}\), where \(n\) is the number of sides. For an octagon, \(n = 8\). So the sum of interior angles is \((8 - 2)\times180^{\circ}=6\times180^{\circ} = 1080^{\circ}\).

Step2: Find the measure of each angle

If each angle is increased by the same amount, and we want to find the measure of the sixth angle. But wait, if it's a regular octagon (assuming all angles are equal as the problem says "each angle is \(1080^{\circ}\)" which is wrong, it should be sum is \(1080^{\circ}\) and for regular octagon each angle is \(\frac{1080^{\circ}}{8}=135^{\circ}\). But maybe the problem has a typo. If we assume it's a regular octagon (all angles equal), then each interior angle is \(\frac{(8 - 2)\times180^{\circ}}{8}=\frac{1080^{\circ}}{8}=135^{\circ}\)

Answer:

\(135\)