Question

question
what is the measure of each interior angle of the regular polygon pictured below? if necessary, round to the nearest tenth.
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Explanation:

Step1: 多边形内角和公式

多边形内角和公式为\((n - 2)\times180^{\circ}\)（\(n\)为边数，\(n\geqslant 3\)且\(n\)为整数）。此图为九边形，即\(n = 9\)。

Step2: 计算内角和

将\(n = 9\)代入公式，内角和\(S=(9 - 2)\times180^{\circ}=7\times180^{\circ}=1260^{\circ}\)。

Step3: 计算单个内角

因为是正多边形，所以每个内角相等，单个内角\(\theta=\frac{1260^{\circ}}{9}=140^{\circ}\)。

Answer:

\(140^{\circ}\)