1.9 线性对等

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  线性对等

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  Linear Pairs
  ::线性对等

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  Two angles are adjacent if they have the same vertex , share a side, and do not overlap.  $\begin{array}{r}\mathrm{\angle }PSQ\end{array}$ and $\begin{array}{r}\mathrm{\angle }QSR\end{array}$ are adjacent.
  ::两个角度相邻,如果两个角度的顶点相同,共用一面,不重叠。 @PSQ 和 @SR 是相邻的。

  

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  A linear pair is two angles that are adjacent and whose non-common sides form a straight line . If two angles are a linear pair, then they are supplementary (add up to $\begin{array}{r}{180}^{\circ }\end{array}$ ). $\begin{array}{r}\mathrm{\angle }PSQ\end{array}$ and $\begin{array}{r}\mathrm{\angle }QSR\end{array}$ are a linear pair.
  ::线性对面是相邻的两个角度,其非共同面构成一条直线线。如果两个角度是线性对,那么它们是补充的(加到180)。 PSQ 和SR 是线性对。

  

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  What if you were given two angles of unknown size and were told they form a linear pair? How would you determine their angle measures?
  ::假若你们获得两个不明的角,并且被告知它们为线性对子,你们如何确定它们的角度呢?

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  Examples
  ::实例

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  For Examples 1 and 2, use the diagram below. Note that $\begin{array}{r}\overline{NK}\perp \stackrel{\leftrightarrow }{IL}\end{array}$ .
  ::例1和例2使用下图。请注意NK L。

  

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  Example 1
  ::例1

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  Name one linear pair of angles.
  ::列出一个直线角度。

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  $\begin{array}{r}\mathrm{\angle }MNL\end{array}$ and $\begin{array}{r}\mathrm{\angle }LNJ\end{array}$
  ::MNLANDLNJ(缅甸)

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  Example 2
  ::例2

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  What is $\begin{array}{r}m\mathrm{\angle }INL\end{array}$ ?
  ::什么是MINL?

  $\begin{array}{r}{180}^{\circ }\end{array}$

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  Example 3
  ::例3

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  What is the measure of each angle?
  ::每个角度的量度是多少?

  

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  These two angles are a linear pair, so they add up to $\begin{array}{r}{180}^{\circ }\end{array}$ .
  ::这两个角度是线性对角, 所以它们加起来等于180。

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  $$\begin{array}{rl}(7q-46{)}^{\circ }+(3q+6{)}^{\circ }& ={180}^{\circ }\\ 10q-{40}^{\circ }& ={180}^{\circ }\\ 10q& ={220}^{\circ }\\ q& ={22}^{\circ }\end{array}$$

  
  :7q-46) (3q+6) (180) (10q)-40(180) (10q)=(220) (q)=(22)

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  Plug in $\begin{array}{r}q\end{array}$ to get the measure of each angle. $\begin{array}{r}m\mathrm{\angle }ABD=7({22}^{\circ })-{46}^{\circ }={108}^{\circ }m\mathrm{\angle }DBC={180}^{\circ }-{108}^{\circ }={72}^{\circ }\end{array}$
  ::Q 中的插件以获得每个角度的量度 。 mABD=7( 22) - 46108 mDBC=18010872

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  Example 4
  ::例4

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  Are $\begin{array}{r}\mathrm{\angle }CDA\end{array}$ and $\begin{array}{r}\mathrm{\angle }DAB\end{array}$ a linear pair? Are they supplementary?
  ::CDA和DAB是线性对吗?

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  The two angles are not a linear pair because they do not have the same vertex. They are supplementary because they add up to $\begin{array}{r}{180}^{\circ }\end{array}$ : $\begin{array}{r}{120}^{\circ }+{60}^{\circ }={180}^{\circ }\end{array}$ .
  ::这两个角度不是线性对, 因为它们没有相同的顶点。 它们具有补充性, 因为它们加起来等于 180 : 120 60 180 。

  

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  Example 5
  ::例5

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  Find the measure of an angle that forms a linear pair with $\begin{array}{r}\mathrm{\angle }MRS\end{array}$ if $\begin{array}{r}m\mathrm{\angle }MRS\end{array}$ is $\begin{array}{r}{150}^{\circ }\end{array}$ .
  ::如果 m MRS 是 150 , 则会找到一个角度的量度, 以 QMRS 构成线性对和 QMRS 的线性对 。

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  Because linear pairs have to add up to $\begin{array}{r}{180}^{\circ }\end{array}$ , the other angle must be $\begin{array}{r}{180}^{\circ }-{150}^{\circ }={30}^{\circ }\end{array}$ .
  ::因为线性配对必须加到180, 另一个角度必须是18015030。

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  Review
  ::回顾

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  For 1-5, determine if the statement is true or false.
  ::1-5,确定声明是真实的还是虚假的。

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  1. Linear pairs are congruent.
     ::线性对子是相同的。
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  2. Adjacent angles share a vertex.
     ::相邻角度有一个共同的顶点。
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  3. Adjacent angles overlap.
     ::近角重叠 。
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  4. Linear pairs are supplementary.
     ::线性配对是补充性的。
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  5. Supplementary angles form linear pairs.
     ::补充角度形成线性对子。

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  For exercise 6, find the value of $\begin{array}{r}x\end{array}$ .
  ::对于练习6, 找到 x 的值 。

  6. 

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  Find the measure of an angle that forms a linear pair with $\begin{array}{r}\mathrm{\angle }MRS\end{array}$ if $\begin{array}{r}m\mathrm{\angle }MRS\end{array}$ is:
  ::如果 mMRS 是 , 则查找以 {MRS 构成 MRS 成线性对的角的量度 :

  7. $\begin{array}{r}{61}^{\circ }\end{array}$
  8. $\begin{array}{r}{23}^{\circ }\end{array}$
  9. $\begin{array}{r}{114}^{\circ }\end{array}$
  10. $\begin{array}{r}{7}^{\circ }\end{array}$
  11. $\begin{array}{r}{179}^{\circ }\end{array}$
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  12. $\begin{array}{r}{z}^{\circ }\end{array}$
      ::

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  Review (Answers)
  ::回顾(答复)

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  Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。