1.8 补充角

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  补充角度

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  Supplementary Angles
  ::补充角度

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  Two angles are supplementary if they add up to $\begin{array}{r}{180}^{\circ }\end{array}$ . Supplementary angles do not have to be congruent or adjacent.
  ::两个角度如果加起来等于 180 则是补充的。 补充角度不必是一致或相邻的 。

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  What if you were given two angles of unknown size and were told they are supplementary? How would you determine their angle measures?
  ::假若给你们两个尺寸不明的角度,并被告知它们是补充的,你们如何确定它们的角度量度呢?

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  Examples
  ::实例

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  Example 1
  ::例1

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  Find the measure of an angle that is supplementary to $\begin{array}{r}\mathrm{\angle }ABC\end{array}$ if $\begin{array}{r}m\mathrm{\angle }ABC\end{array}$ is  $\begin{array}{r}{118}^{\circ }\end{array}$ .
  ::如果 m ABC 是 118 , 则查找对 ABC 的补充角的量度 。

  $\begin{array}{r}{180}^{\circ }-{118}^{\circ }={62}^{\circ }\end{array}$ .

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  Example 2
  ::例2

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  Find the measure of an angle that is supplementary to  $\begin{array}{r}\mathrm{\angle }ABC\end{array}$  if $\begin{array}{r}m\mathrm{\angle }ABC\end{array}$  is  $\begin{array}{r}{32}^{\circ }\end{array}$ .
  ::找到一个对 ABC 的补充角度的量度,如果 m ABC 是 32 。

  $\begin{array}{r}{180}^{\circ }-{32}^{\circ }={148}^{\circ }\end{array}$ .

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  Example 3
  ::例3

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  The two angles below are supplementary. If $\begin{array}{r}m\mathrm{\angle }MNO={78}^{\circ }\end{array}$ what is $\begin{array}{r}m\mathrm{\angle }PQR\end{array}$ ?
  ::下面的两个角度是补充的。 如果 mMNO=78 什么是 mPQR?

  

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  Set up an equation. However, instead of equaling $\begin{array}{r}{90}^{\circ }\end{array}$ , now the sum is $\begin{array}{r}{180}^{\circ }\end{array}$ .
  ::设置一个方程。然而,与其说等于90, 不如说是180。

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  $$\begin{array}{rl}{78}^{\circ }+m\mathrm{\angle }PQR& ={180}^{\circ }\\ m\mathrm{\angle }PQR& ={102}^{\circ }\end{array}$$

  
  ::78PQR=180mPQR=102

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  Example 4
  ::例4

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  What are the measures of two congruent, supplementary angles?
  ::用两个一致的补充角度衡量是什么?

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  Supplementary angles add up to $\begin{array}{r}{180}^{\circ }\end{array}$ . Congruent angles have the same measure. So, $\begin{array}{r}{180}^{\circ }÷2={90}^{\circ }\end{array}$ , which means two congruent, supplementary angles are right angles, or $\begin{array}{r}{90}^{\circ }\end{array}$ .
  ::补充角度加起来等于180。 共角角度具有相同的度量。 所以, 1802=90, 意思是两个相近的, 补充角度是右角, 或90 。

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  Example 5
  ::例5

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  Find the measure of an angle that is a supplementary to $\begin{array}{r}\mathrm{\angle }MRS\end{array}$ if $\begin{array}{r}m\mathrm{\angle }MRS\end{array}$ is $\begin{array}{r}{70}^{\circ }\end{array}$ .
  ::如果MZMS为 70, 则查找一个角度的量度, 该角度是 QMRS 的补充 。

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  Because supplementary angles have to add up to $\begin{array}{r}{180}^{\circ }\end{array}$ , the other angle must be $\begin{array}{r}{180}^{\circ }-{70}^{\circ }={110}^{\circ }\end{array}$ .
  ::因为补充角度加起来必须达到180, 另一个角度必须是18070110。

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  Review
  ::回顾

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  Find the measure of an angle that is supplementary to $\begin{array}{r}\mathrm{\angle }ABC\end{array}$ if $\begin{array}{r}m\mathrm{\angle }ABC\end{array}$ is:
  ::查找对 ABC 补充的角的测量值,如果 m ABC 是 :

  1. $\begin{array}{r}{114}^{\circ }\end{array}$
  2. $\begin{array}{r}{11}^{\circ }\end{array}$
  3. $\begin{array}{r}{91}^{\circ }\end{array}$
  4. $\begin{array}{r}{84}^{\circ }\end{array}$
  5. $\begin{array}{r}{57}^{\circ }\end{array}$
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  6. $\begin{array}{r}{x}^{\circ }\end{array}$
     ::x
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  7. $\begin{array}{r}(x+y{)}^{\circ }\end{array}$
     :x+y)____________________________________________________________________________________

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  Use the diagram below for exercises 8-9. Note that $\begin{array}{r}\overline{NK}\perp \stackrel{\leftrightarrow }{IL}\end{array}$ .
  ::练习 8- 9 使用下图。 请注意 NK L 。

  

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  8. Name two supplementary angles.
     ::列出两个补充角度 。

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  9. If $\begin{array}{r}m\mathrm{\angle }INJ={63}^{\circ }\end{array}$ , find $\begin{array}{r}m\mathrm{\angle }JNL\end{array}$ .
     ::如果MINJ=63, 找到MJNL。

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  For exercise 10, determine if the statement is true or false.
  ::第10项练习,确定声明是真实的还是虚假的。

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  10. Supplementary angles add up to $\begin{array}{r}{180}^{\circ }\end{array}$ .
      ::补充角度加起来等于180。

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  For 11-12, find the value of $\begin{array}{r}x\end{array}$ .
  ::对于 11-12, 找到 x 的值 。

  11. 
  12. 

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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 。

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  Resources
  ::资源