初二数学寒假作业 求各位帮下忙 1.一个多边形除了一个内角外,其余各内角之和为1190度,则这个内

2025-03-15 02:53:46
推荐回答(2个)
回答1:

第一题:
1190÷180=6……110
180-110=70°
答:这个内角是70度。
第二题:
设这个多边形的边数为n
n(n-3)÷2=3n
n(n-3)=6n
n²-n-9n=0
n²-9n=0
n(n-9)=0
n=0(舍去)
n-9=0,n=9
答:这个多边形的边数是9。
第三题:
证明:
∵a²+b²+c²=ab+bc+ac
∴2a²+2b²+2c²=2ab+2bc+2ac
∴2a²+2b²+2c²-2ab-2bc-2ac=0
(a²-2ab+b²)+(b²-2bc+c²)+(a²-2ac+c²)=0
(a-b)²+(b-c)²+(a-c)²=0
∴a-b=0,a=b
b-c=0,b=c
a-c=0,a=c
∴a=b=c
∴△ABC是等边三角形。

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回答2:

根据内角和公式讨论吧

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