1.
(2020·浙江模拟)
取一张边长为4的正方形纸折五角星.操作步骤如下:
①按如图1、图2的方法对折两次,将图2展开后得到图3;
②如图4所示折出正方形ABCD对角线的交点O,将纸片折叠,使得点H与点O重合,折痕为EF,再将四边形EFOG折叠,使得EF与FO重合;
③最后再将∠CFO沿着FO折叠,得到图5,沿图中虚线PM剪一刀.展开得图6.
![](//tikupic.21cnjy.com/33/89/33897b604940c77cb2d6c12e9d62333b.jpg)
![](//tikupic.21cnjy.com/76/97/76977ba9b24ac77fe9752962fe17fc60.jpg)
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(1)
若图6中∠ABC=36°,则图5中∠MPN=°;
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(2)
小王认为此时∠OFC=36°.小黄同学提出了质疑!若已知sin36°=
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmrow%3E%3Cmsqrt%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmsqrt%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
.请求出sin∠OFC=
,这样就可以知道谁的判断是正确的.
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