如图,点O是直线
上一点,以O为顶点作
,且
、
位于直线
两侧,
平分
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/3fe3877c-a6c6-49f8-8d36-7f69a6013f73.png?resizew=157)
(1)当
时
①求
的度数;
②求
和
的度数;
(2)当
时,直接写出
的度数(用含
的式子表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ccc37b189fa2cbc269ca0b233dac37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed66570f697459aba9daa2eaf9460bcb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/3fe3877c-a6c6-49f8-8d36-7f69a6013f73.png?resizew=157)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/618ede24ca37aa33a3789867be8f66b4.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/418ebb89d29f4f631b055c911e8d178a.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc9f91270ddbe1cf3c1362e1b95aee14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15886bb1365d039d8e4450cae287788d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f435c3556b48f0eccc958240fc6c7d6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15886bb1365d039d8e4450cae287788d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
更新时间:2024-02-04 15:39:33
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解答题-问答题
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【推荐1】如图,
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【推荐2】阅读材料并解答问题.
数学课上,老师给出了如下问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/15/bdf9b979-b4f0-4a86-a773-5bc103bf983e.png?resizew=385)
如图1,
,
平分
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以下是小兰的解答过程(部分空缺):
解:如图2
因为
平分
.
所以
_________
_________.
又因为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b571c587a699f24c1121b09d54f3f2.png)
所以
_________.
张明说:“我觉得这道题有两种情况,小兰考虑的是
在
内部的情况,事实上
还可以在
的外部.”
请完成以下问题:
(1)请你将小兰的解答过程补充完整.
(2)根据张明的想法,请你在图1中画出另一种情况对应的图形,并求此时
的度数.
数学课上,老师给出了如下问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/15/bdf9b979-b4f0-4a86-a773-5bc103bf983e.png?resizew=385)
如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/950a96f120b449d9cf5c1709867c3d2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b571c587a699f24c1121b09d54f3f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed66570f697459aba9daa2eaf9460bcb.png)
以下是小兰的解答过程(部分空缺):
解:如图2
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab8133507183adcd8166f48e8374839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e515787ebe97ed2662237d9ca51ea1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2979f64c85f82d8975d73ee1c342de.png)
又因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b571c587a699f24c1121b09d54f3f2.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45739116f428f7c6c5964de72a1fa101.png)
张明说:“我觉得这道题有两种情况,小兰考虑的是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22df2977de56cc69be0c1e847653d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22df2977de56cc69be0c1e847653d7a.png)
请完成以下问题:
(1)请你将小兰的解答过程补充完整.
(2)根据张明的想法,请你在图1中画出另一种情况对应的图形,并求此时
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解答题-证明题
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【推荐1】如图,
平分
,
,试说明
.
证明:∵
平分
( ),
∴
( ),
又∵
( ),
∴
( ),
∴
( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4189a0821a0ffab9dc171ecd279ba442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e53497af8899cb299d762f1a4f46a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
证明:∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4189a0821a0ffab9dc171ecd279ba442.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/207c37b4e9eb8c53fd2ae13c7afe92dc.png)
又∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e53497af8899cb299d762f1a4f46a55.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1503237215798ab4694f90a3a5390787.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab8099c774a6ae6dd98712b0b90b60cf.png)
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名校
【推荐2】如图,已知
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![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/10/cfcfce6c-9871-47b1-96ff-be7d0e8de13b.png?resizew=148)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e18c7dc38750d0e1787adee0055543d3.png)
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