1 . 如图所示,
是直线
上的一个点,
.
![](https://img.xkw.com/dksih/QBM/2023/9/20/3329041593344000/3329401044287488/STEM/94608e9290d9407990ea8487584c0cb9.png?resizew=175)
(1)写出图中互余的角和互补的角;
(2)若
的余角的3倍比它的补角少
,求
的度数.
思维过程展现:
(1)观察图形,因为
,所以![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b05714b8620eba2f56084a91442533.png)
______________
,则图中互余的角为______________ 与______________ ,互补的角为______________ 与______________ ,______________ 与______________ .
(2)由“
的余角的3倍比它的补角少
”,可以设
,由题意得______________ ,解得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
______________ .所以![](https://staticzujuan.xkw.com/quesimg/Upload/formula/021bc0ff7e36c9d6d70ddd2e51e8c04c.png)
______________
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ba1f04ac2b3498c50c39dfcc1e030be.png)
![](https://img.xkw.com/dksih/QBM/2023/9/20/3329041593344000/3329401044287488/STEM/94608e9290d9407990ea8487584c0cb9.png?resizew=175)
(1)写出图中互余的角和互补的角;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed66570f697459aba9daa2eaf9460bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ccc30d7dcade65397851643a607388c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fed1f57a835af4e9022e27603d12d31.png)
思维过程展现:
(1)观察图形,因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60c7ce98569ab27e5d91f96710592dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b05714b8620eba2f56084a91442533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83873a9d782f2588c5eedbfe73f9bc2f.png)
(2)由“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed66570f697459aba9daa2eaf9460bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ccc30d7dcade65397851643a607388c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075f44f8b8c3d3bf0cd380b7a8f1b8f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/021bc0ff7e36c9d6d70ddd2e51e8c04c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83873a9d782f2588c5eedbfe73f9bc2f.png)
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