Question

exterior angles of polygons
score: 2/3 penalty: 1 off
question
the measures of the exterior angles of a pentagon are x°, 3x°, 4x°, 5x°, and 7x°. find the measure of the largest exterior
angle.
answer attempt 1 out of 2
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Explanation:

Step1: 多边形外角和定理

多边形外角和为\(360^{\circ}\)，已知五边形外角分别为\(x^{\circ}\)，\(3x^{\circ}\)，\(4x^{\circ}\)，\(5x^{\circ}\)，\(7x^{\circ}\)，则\(x + 3x + 4x + 5x + 7x=360\)。

Step2: 求解\(x\)

合并同类项得\(20x = 360\)，两边同时除以\(20\)，即\(x=\frac{360}{20}=18\)。

Step3: 求最大外角

最大外角为\(7x^{\circ}\)，把\(x = 18\)代入，得\(7\times18 = 126\)。

Answer:

\(126\)