Question

question
the measures of the exterior angles of a hexagon are x°, 2x°, 6x°, 8x°, 9x°, and 10x°. find the measure of the smallest exterior angle.
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attempt 1 out of 2
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Explanation:

Step1: 多边形外角和定理

任意多边形的外角和都为\(360^{\circ}\)。
已知六边形外角分别为\(x^{\circ},2x^{\circ},6x^{\circ},8x^{\circ},9x^{\circ},10x^{\circ}\)，则\(x + 2x+6x + 8x+9x + 10x=360\)。

Step2: 求解\(x\)的值

合并同类项：\((1 + 2+6 + 8+9 + 10)x=360\)，即\(36x = 360\)。
两边同时除以\(36\)：\(x=\frac{360}{36}=10\)。

Answer:

\(10\)