Question

what is the measure of each interior angle of the regular polygon pictured below? if necessary, round to the nearest tenth. answer attempt 1 out of 3 submit answer

Explanation:

Step1: 确定多边形的边数

观察图形，这是一个正六边形，所以边数\(n = 6\)。

Step2: 计算内角和

正多边形内角和公式为\((n - 2)\times180^{\circ}\)，将\(n = 6\)代入，得到内角和为\((6 - 2)\times180^{\circ}=4\times180^{\circ} = 720^{\circ}\)。

Step3: 计算每个内角的度数

因为正多边形的每个内角都相等，所以每个内角的度数为内角和除以边数，即\(\frac{(n - 2)\times180^{\circ}}{n}\)，将\(n = 6\)代入，得到\(\frac{720^{\circ}}{6}=120^{\circ}\)。

Answer:

\(120^{\circ}\)