多边形及其内角和A.pdf
1/4 7.3 多边形及其内角和1下面哪一个度数是某个多边形的内角和（）A270 B 630 C1920 D720知识点：多边形的内角和知识点的描述：n 边形的内角和是（n-2）180，多边形的内角和一定是180的整数倍答案：D 详细解答：270、630、1920、720中只有D720是 180的整数倍，所以选D.2.一个多边形的外角中,钝角的个数不可能是()A.1个 B.2个 C.3个 D.4个知识点：多边形的外角和知识点的描述：多边形的外角和360，是一个不变的常数，与边数无关，也就是说不管是几边形，他的外角和总是360答案：D 详细解答：多边形的外角和360，因此一个多边形的外角中,钝角的个数不可能超过3个，如果是4 个钝角，那么外角和大于360，这是不可能的。所以选D。3 若一个正多边形的每一个内角都等于120，则它是（）A正方形 B 正五边形 C 正六边形 D正八边形知识点：正多边形的内角知识点的描述：正多边形的每个内角都相等，正多边形的内角和也是（n-2）180.答案：C 详细解答：若一个正多边形的每一个内角都等于120，那么他的每一个外角都等于60，由于多边形的外角和360，所以边数就是360 60=6.另一种解法：假设正n 边形，（n-2）180=n120，解得n=6。4三角形一个外角小于与它相邻的内角，这个三角形是（）A直角三角形 B锐角三角形 C钝角三角形 D属于哪一类不能确定知识点:三角形的外角和与他相邻的内角的关系.知识点的描述:三角形的外角和与他相邻的内角互补.答案:C 详细解答:三角形的外角和与他相邻的内角互补,又三角形一个外角小于与它相邻的内角,那2/4 么外角是锐角而内角是钝角,所以这个三角形是钝角三角形.5一个多边形的内角和是三角形外角和的3 倍，则这个多边形为（）A五边形 B 六边形 C八边形 D九边形知识点:多边形的内角和与多边形的外角和.知识点的描述:多边形的内角和为（n-2）180,多边形的外角和为360.答案:C 详细解答:多边形的内角和是三角形外角和的3 倍，则（n-2）180=3360,解得 n=8.6.若从一个多边形的一个顶点出发,最多可以引10 条对角线,则它是()A.十三边形 B.十二边形 C.十一边形 D.十边形知识点:多边形的对角线总数知识点的描述:n 边形的每一个顶点都有(n-3)个和他不相邻的顶点,从 n 边形的每一个顶点可以引出(n-3)条对角线,所以 n边形共有32n n条对角线答案:A 详细解答:因为从 n 边形的每一个顶点可以引出(n-3)条对角线,所以 n-3=10,得 n=13.7若三角形三个外角的比为4：2：3，则这个三角形是（）A、锐角三角形B、直角三角形C、等腰三角形D、钝角三角形知识点：三角形的内角和、三角形的外角和知识点的描述：三角形的内角和180，三角形外角和360答案：D 三角形三个外角的比为4：2：3，所以假设三角形的三个外角分别为4k、2k、3k，又因为三角形的外角和360，所以4k+2k+3k=360，解得k=40，所以最小外角是80，那么最大内角100，因此这个三角形是钝角三角形.8.一个多边形除一个内角外，其余各个内角的和为20300，则这个多边形的边数（）A.12 B.13 C.14 D.15 .知识点：多边形的内角和知识点的描述：n 边形的内角和是（n-2）180，多边形的内角和一定是180的整数倍答案：C 详细解答：设边数为n，这个内角为x，则 00 x1800文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z83/4 根据题意，得(n-2)1800=x+20300(n-2)1800是 1800的倍数x+20300必是 1800的倍数203001800=1150 x=1800-500=1300(n-2)1800=180011+1800 n-2=12 n=14 这个多边形的边数为14.点拨：本题在利用多边形的内角和计算公式得到方程后，又借助数的整除，通过讨论得这个内角的度数，这是解决有关多边形的内角和与外角和问题的一种常用的方法.9.一个五边形的五个外角的度数比是12345，这个五边形的五个内角的度数比（）.A.123 45B.5 432 1 C.131197 5D.11 9753 知识点：多边形的外角和相邻的内角的关系，多边形的外角和。知识点的描述：多边形的外角和相邻的内角互补；多边形的外角和360。答案：C 详细解答：五边形的五个外角的度数比是12345，假设这五个外角的度数分别是k、2k、3k、4k、5k，因为外角和为360，所以k+2k+3k+4k+5k=360，求得k=24.五个外角的度数分别是24、48、72、96、120，那么与它们相邻的五个内角的度数分别是156、132、108、84、60，所以五个内角的度数比为156132 108 84 60=1311975 10.已知 ABC的边 BA、BC分别与 DEF的边 ED、EF垂直，垂足分别是M、N,且 ABC=700,则 DEF的度数（）.A.700 B.1100 C.700或 1100 D.1400知识点：多边形内角和定理的综合应用知识点的描述：只要善于从复杂的图形中找到基本图形，利用三角形或多边形的内角和定理就可以解决问题答案：C 点拨：本题已知了ABC和 DEF的边的关系，没有给出图形，可先画出图形，再结合图形，利用相关知识求解.根据题意，符合条件的图形可画出两个，要考虑周全，不能漏解，两个图形：分别如图（1），图（2）在图（1）中，求 DEF,利用四边形内角和定理即可文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z84/4 在图（2）中，求 DEF,利用三角形内角和等于1800，以及利用两个三角形中角的关系进行求解.详细解答：(1)如图（1）DE AB BME=900EFBC BNE=900 B+BME+BNE+DEF=3600 又 B=700 DEF=1100(2)如图（2）DE AB BME=900EFBC BNE=900 BME=BNE DEF+BME+EOM=1800又 B+BNE+BON=1800 DEF+BME+EOM=B+BNE+BON DEF+EOM=B+BON EOM=BON DEF=B B=700 DEF=700 DEF=700或 1100A B F C E D M N（1）（2）A E O B C D M N F 文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8文档编码:CM6N7L4K10X9 HK8T3R10I8W3 ZJ6T9X4P3Z8
