Question

1. cindy tried to find the sum of the exterior angles of the hexagon. what was her error?

180°·(6−2)=720°

Explanation:

Step1: Recall exterior angle sum rule

The formula \(180^\circ\cdot(n - 2)\) is for the sum of interior angles of a polygon with \(n\) sides. For any convex polygon (including a hexagon), the sum of the exterior angles (one at each vertex, measured as the angle you turn when walking around the polygon) is always \(360^\circ\), regardless of the number of sides \(n\) (as long as \(n\geq 3\)).

Step2: Identify Cindy's error

Cindy used the formula for the sum of interior angles (\(180^\circ\cdot(6 - 2)\)) to calculate the sum of exterior angles. She confused the formula for interior angles with the rule for exterior angles. The sum of exterior angles of any polygon (with \(n\geq3\)) is \(360^\circ\), not \(180^\circ\cdot(n - 2)\).

Answer:

Cindy used the formula for the sum of interior angles (\(180^\circ\cdot(6 - 2)\)) instead of the rule that the sum of exterior angles of any polygon is \(360^\circ\). Her error was confusing the formula for interior angles with the exterior angle sum property.