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6．3.2　角的比较与运算
eq \o(\s\up7( INCLUDEPICTURE "知识梳理.tif" INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/知识梳理.tif" \* MERGEFORMAT INCLUDEPICTURE "../../知识梳理.tif" \* MERGEFORMAT INCLUDEPICTURE "../../知识梳理.tif" \* MERGEFORMAT INCLUDEPICTURE "../知识梳理.tif" \* MERGEFORMAT INCLUDEPICTURE "知识梳理.tif" \* MERGEFORMAT ),\s\do5(　　　　　　　))
知识点一　角的大小比较
1．角的大小比较与线段长短的比较类似，方法有两种．
方法1：度量法：直接用量角器度量比较．
注意：角的大小只与角两边的张开程度有关，与两边的长度无关．
方法2：叠合法：把两个角的顶点和一边重合，两个角的另一边放在重合边的同一侧，离重合边越远角度越大，反之越小．
如比较图中角的大小(图1、图2、图3).
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX198.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX198.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX198.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX198.tif" \* MERGEFORMAT INCLUDEPICTURE "SX198.tif" \* MERGEFORMAT
图1
∠AOB＜∠A′O′B′
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX198A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX198A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX198A.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX198A.tif" \* MERGEFORMAT INCLUDEPICTURE "SX198A.tif" \* MERGEFORMAT
图2
∠AOB＝∠A′O′B′
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX198B.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX198B.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX198B.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX198B.tif" \* MERGEFORMAT INCLUDEPICTURE "SX198B.tif" \* MERGEFORMAT
图3
∠AOB＞∠A′O′B′
练习1　用“叠合法”比较∠1与∠2的大小，正确的是(　C　).
eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX199.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX199.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX199.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX199.tif" \* MERGEFORMAT INCLUDEPICTURE "SX199.tif" \* MERGEFORMAT ),\s\do5(A)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX199A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX199A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX199A.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX199A.tif" \* MERGEFORMAT INCLUDEPICTURE "SX199A.tif" \* MERGEFORMAT ),\s\do5(B)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX199b.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX199b.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX199b.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX199b.tif" \* MERGEFORMAT INCLUDEPICTURE "SX199b.tif" \* MERGEFORMAT ),\s\do5(C)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX199C.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX199C.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX199C.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX199C.tif" \* MERGEFORMAT INCLUDEPICTURE "SX199C.tif" \* MERGEFORMAT ),\s\do5(D))
【解析】根据“叠合法”比较∠1与∠2的大小，需∠1和∠2的顶点及其中一边重合，并且另一边在重合边的同侧．故选C.
总结　用“叠合法”比较角的大小时，一定要使两个角的顶点及一边重合，另一边落在重合边的同一侧，然后根据边的位置判断大小；也可以用纸板做成模型，移动纸板，进行比较．
知识点二　角度的运算
练习2　如图所示，∠BOC＋∠DOC＝∠BOD，∠BOC＝∠BOD－∠COD，∠AOD＝∠AOB＋∠COD＋∠BOC，∠DOB＝∠DOA－∠COA＋∠BOC．
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX201.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX201.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX201.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX201.tif" \* MERGEFORMAT INCLUDEPICTURE "SX201.tif" \* MERGEFORMAT
总结　角的和与差仍是一个角，只不过是这个角的度数等于另外两个角度数的和或差．
知识点三　角的平分线
2．一般地，从一个角的顶点出发，把这个角分成两个相等的角的射线，叫作这个角的平分线．
练习3　下列关于角的平分线的说法中，正确的是(　D　).
A．角的平分线是平分这个角的一条直线
B．以一个角的顶点为端点且把这个角分成相等的两个角的一条线段
C．角的平分线是一条线段
D．以一个角的顶点为端点且把这个角分成相等的两个角的一条射线
总结　角的平分线必须满足三个条件：一是从角的顶点引出的射线，二是在角的内部，三是把已知角分成两个相等的角，不能只凭倍数来判断．
eq \o(\s\up7( INCLUDEPICTURE "课后练习.tif" INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/课后练习.tif" \* MERGEFORMAT INCLUDEPICTURE "../../课后练习.tif" \* MERGEFORMAT INCLUDEPICTURE "../../课后练习.tif" \* MERGEFORMAT INCLUDEPICTURE "../课后练习.tif" \* MERGEFORMAT INCLUDEPICTURE "课后练习.tif" \* MERGEFORMAT ),\s\do5(　　　　　　　))
INCLUDEPICTURE "三角.tif" INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "三角.tif" \* MERGEFORMAT 基础巩固
1．已知∠α＝30°18′，∠β＝30.18°，∠γ＝30.3°，则相等的两个角是(　A　).
A．∠α和∠γ B．∠β和∠γ
C．∠α和∠β D．无法确定
2.如图，OB是∠AOC的平分线，∠COD＝∠BOD，∠COD＝16°，则∠AOD的度数是(　C　).
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX204.TIF" \* MERGEFORMAT INCLUDEPICTURE "../../SX204.TIF" \* MERGEFORMAT INCLUDEPICTURE "../../SX204.TIF" \* MERGEFORMAT INCLUDEPICTURE "../SX204.TIF" \* MERGEFORMAT INCLUDEPICTURE "SX204.TIF" \* MERGEFORMAT
A．64° B．70°
C．80° D．85°
【解析】因为∠COD＝∠BOD，∠COD＝16°，
所以∠BOC＝2∠COD＝2×16°＝32°.
因为OB是∠AOC的平分线，
所以∠AOC＝2∠BOC＝2×32°＝64°，
所以∠AOD＝∠AOC＋∠COD＝64°＋16°＝80°.故选C.
3．如图，直线AB，CD相交于点O，OE是∠BOC的平分线，且∠BOE＝48°，那么∠AOC＝(　A　).
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX205.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX205.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX205.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX205.tif" \* MERGEFORMAT INCLUDEPICTURE "SX205.tif" \* MERGEFORMAT
A.84° B．95°
C．105° D．125°
【解析】因为OE是∠BOC的平分线，所以∠BOC＝2∠BOE＝96°，
所以∠AOC＝180°－∠BOC＝84°.
故选A.
4.如图，两个直角∠AOB，∠COD有相同的顶点O，下列结论：①∠AOC＋∠BOD＝90°；②∠AOC＝∠BOD；③若OC平分∠AOB，则OB平分∠COD；④∠AOD的平分线与∠COB的平分线是同一条射线．其中正确的有(　B　).
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX206.TIF" \* MERGEFORMAT INCLUDEPICTURE "../../SX206.TIF" \* MERGEFORMAT INCLUDEPICTURE "../../SX206.TIF" \* MERGEFORMAT INCLUDEPICTURE "../SX206.TIF" \* MERGEFORMAT INCLUDEPICTURE "SX206.TIF" \* MERGEFORMAT
A．4个 B．3个
C．2个 D．1个
【解析】①因为只有当OC，OB分别为∠AOB和∠COD的平分线时，∠AOC＋∠BOD＝90°，
所以①错误；
②因为∠AOB＝∠COD＝90°，
所以∠AOC＝90°－∠BOC，∠BOD＝90°－∠BOC，
所以∠AOC＝∠BOD，
所以②正确；
③因为∠AOB＝∠COD＝90°，OC平分∠AOB，
所以∠AOC＝∠COB＝45°，
则∠BOD＝90°－45°＝45°，
所以OB平分∠COD，所以③正确；
④因为∠AOC＝∠BOD(已证)，
所以∠AOD的平分线与∠COB的平分线是同一条射线，所以④正确．
故选B.
5．如图，将一张长方形纸按照如图所示的方法对折，两条虚线为折痕，则这两条折痕构成的角的度数是(　A　).
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX207.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX207.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX207.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX207.tif" \* MERGEFORMAT INCLUDEPICTURE "SX207.tif" \* MERGEFORMAT
A．90° B．75°
C．45° D．30°
【解析】如图．
INCLUDEPICTURE "SX207答.tif" INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX207答.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX207答.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX207答.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX207答.tif" \* MERGEFORMAT INCLUDEPICTURE "SX207答.tif" \* MERGEFORMAT
由题意，得∠1＝∠2，∠3＝∠4.
又因为∠1＋∠2＋∠3＋∠4＝180°，
所以∠2＋∠3＝90°，
即这两条折痕构成的角的度数是90°.
故选A.
INCLUDEPICTURE "三角.tif" INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "三角.tif" \* MERGEFORMAT 能力达标
6．如图，已知∠AOB＝35°，∠BOC＝3∠AOB，OD平分∠AOC，求∠COD的度数．
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX209.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX209.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX209.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX209.tif" \* MERGEFORMAT INCLUDEPICTURE "SX209.tif" \* MERGEFORMAT
【解】因为∠BOC＝3∠AOB，∠AOB＝35°，
所以∠BOC＝105°，
所以∠AOC＝∠AOB＋∠BOC＝35°＋105°＝140°.
因为OD平分∠AOC，
所以∠COD＝∠AOC＝70°.
7．已知OB是∠AOC内部的一条射线，OM是∠AOB内部的一条射线，ON是∠BOC内部的一条射线．
eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX210.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX210.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX210.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX210.tif" \* MERGEFORMAT INCLUDEPICTURE "SX210.tif" \* MERGEFORMAT ),\s\do5(图1)) 　　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX211.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX211.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX211.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX211.tif" \* MERGEFORMAT INCLUDEPICTURE "SX211.tif" \* MERGEFORMAT ),\s\do5(图2))
(1)如图1，若∠AOB＝34°，∠BOC＝112°，OM，ON分别是∠AOB，∠BOC的平分线，求∠MON的度数．
(2)如图2，若OB平分∠AOC，且∠CON＝2∠AOM，∠BOM∶∠AOC＝2∶5，则∠BOM和∠BON之间存在怎样的数量关系？请说明理由．
【解】(1)因为∠AOB＝34°，∠BOC＝112°，OM，ON分别是∠AOB，∠BOC的平分线，
所以∠BOM＝∠AOB＝17°，
∠BON＝∠BOC＝56°，
所以∠MON＝∠BOM＋∠BON＝17°＋56°＝73°.
(2)∠BOM∶∠BON＝4∶3.
理由如下：
因为∠CON＝2∠AOM，
所以设∠AOM＝α，则∠CON＝2α，
设∠BOM＝x，
因为OB平分∠AOC，
所以α＋x＝∠BON＋2α，
所以∠BON＝x－α.
因为∠BOM∶∠AOC＝2∶5，
所以x∶(α＋x＋x－α＋2α)＝2∶5，
所以x＝4α，即∠BOM＝4α，
则∠BON＝3α，
所以∠BOM∶∠BON＝4∶3.
INCLUDEPICTURE "三角.tif" INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "三角.tif" \* MERGEFORMAT 挑战创新
8．(分类讨论思想)小英对角平分线兴趣浓厚，小云和她一起探究以下问题．已知∠AOB＝100°，射线OE，OF分别是∠AOC和∠BOC的平分线．
eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX214.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX214.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX214.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX214.tif" \* MERGEFORMAT INCLUDEPICTURE "SX214.tif" \* MERGEFORMAT ),\s\do5(图1)) 　　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX214a.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX214a.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX214a.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX214a.tif" \* MERGEFORMAT INCLUDEPICTURE "SX214a.tif" \* MERGEFORMAT ),\s\do5(图2)) 　　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX214b.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX214b.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX214b.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX214b.tif" \* MERGEFORMAT INCLUDEPICTURE "SX214b.tif" \* MERGEFORMAT ),\s\do5(图3))
(1)如图1，若射线OC在∠AOB的内部，且∠AOC＝36°，求∠EOF的度数；
(2)如图2，若射线OC在∠AOB的内部绕点O旋转，求∠EOF的度数；
(3)若射线OC在∠AOB的外部绕点O旋转(旋转中∠AOC，∠BOC均为小于180°的角)，其余条件不变，请借助图3探究∠EOF的大小．
【解】(1)因为∠AOB＝100°，
∠AOC＝36°，
所以∠BOC＝∠AOB－∠AOC＝64°.
因为射线OE，OF分别是∠AOC和∠BOC的平分线，
所以∠EOC＝∠AOC＝18°，
∠FOC＝∠BOC＝32°，
所以∠EOF＝∠EOC＋∠FOC＝18°＋32°＝50°.
(2)因为射线OE，OF分别是∠AOC和∠BOC的平分线，
所以∠EOC＝∠AOC，∠FOC＝∠BOC，
所以∠EOF＝∠EOC＋∠FOC＝(∠AOC＋∠BOC)＝∠AOB＝×100°＝50°.
(3)①射线OE，OF只有1条在∠AOB外部．若OE在∠AOB外部，如图1.
则∠EOF＝∠FOC－∠COE＝
∠BOC－∠AOC＝(∠BOC－∠AOC)＝∠AOB＝×100°＝50°；
若OF在∠AOB外部，同理，可得∠EOF＝50°.
eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX302.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX302.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX302.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX302.tif" \* MERGEFORMAT INCLUDEPICTURE "SX302.tif" \* MERGEFORMAT ),\s\do5(图1)) 　　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX303.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX303.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX303.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX303.tif" \* MERGEFORMAT INCLUDEPICTURE "SX303.tif" \* MERGEFORMAT ),\s\do5(图2))
②射线OE，OF都在∠AOB外部，如图2.
则∠EOF＝∠EOC＋∠COF＝
∠AOC＋∠BOC＝
(∠AOC＋∠BOC)＝
(360°－∠AOB)＝×260°＝130°.
综上，∠EOF的度数是50°或130°.6．3.2　角的比较与运算
eq \o(\s\up7(),\s\do5(　　　　　　　))
知识点一　角的大小比较
1．角的大小比较与线段长短的比较类似，方法有两种．
方法1：度量法：直接用量角器度量比较．
注意：角的大小只与角两边的张开程度有关，与两边的长度无关．
方法2：叠合法：把两个角的顶点和一边重合，两个角的另一边放在重合边的同一侧，离重合边越远角度越大，反之越小．
如比较图中角的大小(图1、图2、图3).
图1
∠AOB＜∠A′O′B′
图2
∠AOB＝∠A′O′B′
图3
∠AOB＞∠A′O′B′
练习1　用“叠合法”比较∠1与∠2的大小，正确的是(　).
eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( ))
知识点二　角度的运算
练习2　如图所示，∠BOC＋∠DOC＝∠BOD，∠BOC＝∠BOD－∠COD，∠AOD＝∠AOB＋∠COD＋∠BOC，∠DOB＝∠DOA－∠COA＋∠BOC．
知识点三　角的平分线
2．一般地，从一个角的顶点出发，把这个角分成两个相等的角的射线，叫作这个角的平分线．
练习3　下列关于角的平分线的说法中，正确的是(　).
A．角的平分线是平分这个角的一条直线
B．以一个角的顶点为端点且把这个角分成相等的两个角的一条线段
C．角的平分线是一条线段
D．以一个角的顶点为端点且把这个角分成相等的两个角的一条射线
eq \o(\s\up7(),\s\do5(　　　　　　　))
基础巩固
1．已知∠α＝30°18′，∠β＝30.18°，∠γ＝30.3°，则相等的两个角是(　).
A．∠α和∠γ B．∠β和∠γ
C．∠α和∠β D．无法确定
2.如图，OB是∠AOC的平分线，∠COD＝∠BOD，∠COD＝16°，则∠AOD的度数是(　).
A．64° B．70°
C．80° D．85°
3．如图，直线AB，CD相交于点O，OE是∠BOC的平分线，且∠BOE＝48°，那么∠AOC＝(　).
A.84° B．95°
C．105° D．125°
4.如图，两个直角∠AOB，∠COD有相同的顶点O，下列结论：①∠AOC＋∠BOD＝90°；②∠AOC＝∠BOD；③若OC平分∠AOB，则OB平分∠COD；④∠AOD的平分线与∠COB的平分线是同一条射线．其中正确的有(　).
A．4个 B．3个
C．2个 D．1个
5．如图，将一张长方形纸按照如图所示的方法对折，两条虚线为折痕，则这两条折痕构成的角的度数是(　).
A．90° B．75°
C．45° D．30°
能力达标
6．如图，已知∠AOB＝35°，∠BOC＝3∠AOB，OD平分∠AOC，求∠COD的度数．
7．已知OB是∠AOC内部的一条射线，OM是∠AOB内部的一条射线，ON是∠BOC内部的一条射线．
eq \o(\s\up7(),\s\do5(图1)) 　　 eq \o(\s\up7(),\s\do5(图2))
(1)如图1，若∠AOB＝34°，∠BOC＝112°，OM，ON分别是∠AOB，∠BOC的平分线，求∠MON的度数．
(2)如图2，若OB平分∠AOC，且∠CON＝2∠AOM，∠BOM∶∠AOC＝2∶5，则∠BOM和∠BON之间存在怎样的数量关系？请说明理由．
挑战创新
8．(分类讨论思想)小英对角平分线兴趣浓厚，小云和她一起探究以下问题．已知∠AOB＝100°，射线OE，OF分别是∠AOC和∠BOC的平分线．
eq \o(\s\up7(),\s\do5(图1)) 　　 eq \o(\s\up7(),\s\do5(图2)) 　　 eq \o(\s\up7(),\s\do5(图3))
(1)如图1，若射线OC在∠AOB的内部，且∠AOC＝36°，求∠EOF的度数；
(2)如图2，若射线OC在∠AOB的内部绕点O旋转，求∠EOF的度数；
(3)若射线OC在∠AOB的外部绕点O旋转(旋转中∠AOC，∠BOC均为小于180°的角)，其余条件不变，请借助图3探究∠EOF的大小．

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