每一个内角等于什么是内角,它的中心角等于什

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正八边形的一个内角等于______,它的中心角等于______.
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∵正八边形的每个外角为:360°÷8=45°,∴每个内角为180°-45°=135°;正八边形的中心角为:
=45°.故答案为:135°;45°.
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如果正多边形的中心角等于30°,那么它的每个内角为______度.
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由于正多边形的中心角等于30°,360÷30°=12,所以正多边形为正12边形,又因为其外角和为360°,所以其外角为360÷12=30°,其每个内角为180°-30°=150.
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根据正多边形的中心角为30°,求出正多边形的边数,再求出其每个外角,即可根据内角和外角的和为180度求出每个内角的度数.
本题考点:
正多边形和圆.
考点点评:
本题考查学生对正多边形的概念掌握和计算的能力.解答这类题往往一些学生因对正多边形的基本知识不明确,将多边形的中心角和外角、内角混淆.
正12边形,每角为150度
360/n=30n=12(边形)故它的每个内角为(12-2)180/12=(度)
150 对应正12多边形
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