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are there two x's and two y's? solving for x&ythe problem is two lines that...

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notevenaking | Student, Grade 9 | eNotes Newbie

Posted September 16, 2012 at 8:58 AM via web

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are there two x's and two y's? solving for x&y

the problem is two lines that intersect. two angles across from each other are  y+75 &3y+5. the other two angles across from each other are 3x+7&5x-35.

Tagged with angles, geometry, math, x&y

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted September 16, 2012 at 9:31 AM (Answer #1)

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No if two lines intercepts we have two angles at the interception point. But if we add these two angles what will it become. Here see the example.

 

 

We have two angles at the interception point. One is formed by the red dot, interception point and green dot. The other one is formed by red dot, interception point and white open dot.

just add these two angles. What will it be. The addition is 180 deg.

So for your question;

 (y+75)+(3y+5) = 180 ---(1)

(3x+7)+(5x-35) = 180 ---(2)

 

From (1)

(y+75)+(3y+5) = 180

             4y+80 = 180

                    y = 25

 

From (2)

(3x+7)+(5x-35) = 180

             8x-28   = 180

                      x = 26

 

So the angles are;

(25+75) = 100

(3*25+5) = 80

(3*26+7) = 85

(5*26-35) = 95

 

So the interception angles are 100,80 and 85,95

 

Sources:

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vinish | Student , Undergraduate | Valedictorian

Posted September 16, 2012 at 4:10 PM (Answer #2)

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When you add the two angles which are across each other, you will get 180 for both...

So,

(y+75)+(3y+5)=180 --- (1)

(3x+7)+(5x-35)=180 --- (2)

Now, you must solve these two equations...

From(1)

(y+75)+(3y+5)=180

4y+80=180

4y=180-80

    =100

y=100/4

  =25

 

From(2)

(3x+7)+(5x-35)=180

8x-28=180

8x=180+28

    =208

x=208/8

  =26

 

You are asked to find the values of x and y...

Therefore,

x=26 and y=25

 

If you want to find the values of the angles, you just have to replace x by 26 and y by 25

 

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