给定四边形的角度测量

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Ivonne is a farmer. She plants a rhombus-shaped section of corn each year. This year, she has decided to check the  angles  at each  vertex  of the corn. She determines that one angle is 110 degrees and the another angle is 70 degrees. Her daughter tells her that she can determine the other angle measures without walking around to them. What are the other angle measures?
::Ivonne是农民,她每年种植玉米的一小块红外线。今年,她决定检查玉米每个顶端的角。她确定一个角为110度,另一个角为70度。她女儿告诉她,她可以确定其他角度量,而不必走近它们。其他角度量又是什么?

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In this concept, you will learn how to work with the angle measures of a  quadrilateral .

::在这个概念中,你会学会如何与四边形的角度量法合作。

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Measuring Angles in Quadrilaterals
::测量四方中的角

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Let's look at a  square .
::让我们看看一个广场。

 

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A square has four right angles. Each  right angle  is  $\begin{array}{r}{90}^{\circ }\end{array}$ . You can add up the sum of the  interior angles  of a square and see how this is related to all quadrilaterals.
::方形有四个右角度。 每个右角度为 90 。 您可以将方形内部角度的总和相加, 并查看它与所有四边形的关系 。

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The sum of the interior angles of all quadrilaterals is  $\begin{array}{r}{360}^{\circ }\end{array}$ .
::所有四边形的内部角度之和是360 。

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You can use this information to find the  measure  of missing angles.
::您可以使用此信息查找缺失角度的度量 。

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Write an equation using the variable and given measurements and figure out the measure of the missing angle.
::使用变量和给定的量度写一个方程式, 并找出缺失角度的度量 。

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The missing angle is equal to  $\begin{array}{r}{100}^{\circ }\end{array}$ .
::缺失角度等于 100 。

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Use this information to help you when figuring out missing angle measures in different quadrilaterals.
::使用此信息来帮助您了解不同四边形中缺少的角度量 。

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Also, you can draw specific quadrilaterals using a ruler and a  protractor . Use the protractor to be sure that your work is accurate. This is especially important when drawing squares or   or any figure with a right angle.
::另外,您还可以使用标尺和减量器绘制特定的四边形。使用减量器可以确定您的工作是否准确。在绘制正方形或任何带有正确角度的图形时,这一点特别重要。

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Start by using a protractor to draw in each of the four right angles. By using a ruler and a protractor, your lines will be straight and we will be able to determine that we have drawn the square correctly.
::开始使用一个减号来绘制四个右角度的每一个。 通过使用标尺和减号, 您的线条将会是直的, 我们将能够确定我们已经正确绘制了正方形 。

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Drawing it freehand may seem easier, but it does not assure accuracy! The best way to be sure that your work is accurate is to use a protractor and a ruler.
::绘制它似乎更容易, 但它不能保证准确性! 确定你的工作是否准确的最佳方法是使用一个减速器和一个标尺 。

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Here is the first angle of a square. Now turn the protractor upside down and draw the other angle.
::这是方形的第一个角度。 现在将减速器向下翻转, 并绘制另一个角度 。

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Here is the final figure.
::这是最后的数字。

 

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Examples
::实例

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Example 1
::例1

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Earlier, you were given a problem about Ivonne and her rhombus-shaped field of corn.
::早些时候,你被问及Ivonne 和她的胸罩状玉米田的问题。

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Ivonne knows that one of the angles of the field is 110 degrees and a different angle is 80 degrees. What are the other angle measures?
::Ivonne知道球场的一个角度是 110 度,另一个角度是 80 度。其他角度的量度是什么?

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First, note the properties of angles in a  rhombus .
::首先,注意圆柱形中角度的属性。

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Opposite  sides are  congruent
::对面两面是一致的

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Next, list all of the angle values.
::下一步,列出所有角度值。

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80, 80, 110, and 110
::80、80、110和110

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Then, state the other angle measures.
::然后,请说明其他角度措施。

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80 and 110
::80和110

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The answer is 80 degrees and 110 degrees.
::答案是80度和110度

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Example 2
::例2

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A quadrilateral has the following angle measures: 130, 80 and 95. What is the measure of the missing angle?
::四边形有以下角度量:130、80和95。 缺失角的度量是多少?

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First, write an equation.
::首先,写一个方程。

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  $\begin{array}{r}130+80+95+x=360\end{array}$
::130+80+95+x=360

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Then, solve for the missing angle.
::那么,解决丢失的角度。

55

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The answer is 55 degrees.
::答案是55摄氏度

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Example 3
::例3

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If one angle of a  rectangle  is 90 degrees, what are the measures of the other three angles?
::如果矩形的一个角为90度,其他三个角的度量是多少?

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First, remember the angle rules for a rectangle.
::首先,记住矩形角规则。

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All of the angles are 90 degrees
::所有角度均为90度

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Then, state the measures of the other angles,
::然后,说明其他角度的测量结果,

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90 degrees
::90度 90度

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The answer is 90 degrees.
::答案是90摄氏度

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Example 4
::例4

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A quadrilateral has the following angle measures: 105, 90 and 88. What is the measure of the missing angle?
::四边形有以下角度量:105、90和88。 缺失角的度量是多少?

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First, write an equation.
::首先,写一个方程。

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$\begin{array}{r}105+90+88+x=360\end{array}$
::105+90+88+x=360

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Then, solve for the missing angle.
::那么,解决丢失的角度。

77

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The answer is 77 degrees.
::答案是77摄氏度

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Example 5
::例5

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A   has two congruent angles that are both 85 degrees. The other two angles are congruent. What is the measure of each missing angle?
::A 有两个相近角度, 两者均为 85 度。 另外两个角度是 85 度。 每个缺失角度的度量是多少 ?

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First, write an equation.
::首先,写一个方程。

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  $\begin{array}{r}85+85+x+x=360\end{array}$
::85+85+xx+xx=360

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Next, simplify the equation.
::接下来,简化方程

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  $\begin{array}{r}170+2x=360\end{array}$
::170 + 2 x = 360

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Then, solve for the missing angle.
::那么,解决丢失的角度。

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  $\begin{array}{r}2x=190\end{array}$
::2x=190

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  $\begin{array}{r}x=95\end{array}$
::x = 95

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The answer is 95 degrees.
::答案是95摄氏度

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Review
::回顾

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Answer each of the following questions about quadrilaterals.
::回答以下关于四边形的每一个问题。

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1. True or false. A quadrilateral will always have only four sides.
   ::圆四边永远只有四面
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2. The interior angles of a quadrilateral add up to be _________ degrees.
   ::四边形的内角加起来等于 ° 度。
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3. A square will have four ___________ degree angles.
   ::方形将具有四个度角。
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4. A rectangle will have four ___________ degree angles.
   ::矩形将具有 4 ° 度角度。
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5. True or false. A rhombus will also always have four right angles.
   ::暴风车也总是有四个正确角度
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6. If the sum of three of the angles of a quadrilateral is equal to  $\begin{array}{r}{300}^{\circ }\end{array}$ , it means that the measure of the missing angle is ____________.
   ::如果四边形角的三角之和等于300 ,这意味着缺失角的量度为 。

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What is the value of  $\begin{array}{r}x?\end{array}$
::x 值是多少 ?

7. 

8.

9.

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10. What are all four angles of this rectangle equal to?
::10. 这个矩形的四个角度都等于什么?

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11. How many degrees are in a triangle?
    ::三角形中有多少度?
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12. Write an equation to show how the angles of the two triangles are equal to 360 degrees.
    ::写入一个方程式以显示两个三角形的角度如何等于 360 度。

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Identify the following figures.
::确定下列数字。

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13. 

    [Figure 11]
    
    ::[表11]
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14. 

    [Figure 12]
    
    ::[图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