+0  
 
0
50
4
avatar

Find the values of x and y that make Line 1 || Line 2 and Line 3 || Line 4.

 

 Apr 11, 2022
 #1
avatar+1384 
+1

We know that \((5x + 2y - 25) + z = 180\)

 

Solving for z, we find that \(z = 205 - 5x - 2y\)

 

Using, alternate interior angles, we know that \(2y + x + y + 205 - 5x - 2y = 180\)

 

Simplifying, we find that \(25 = 4x - y\)

 

Because we want \(L_4\) to be parallel to \(L_3\), the angles must be equal, meaning:  \(2y = 4x + 10 \)

 

We now have a system of equations to solve: \(2y = 4x +10\) and \(25 = 4x - y\)

 

Solving, we find \(\color{brown}\boxed{x =15, \space y = 35}\)

 Apr 11, 2022
 #3
avatar
0

Thank you so much!

Guest Apr 11, 2022
 #2
avatar+122390 
+1

If L3  is parallel to L4, then, by corresponding angles

 

4x + 10  = 2y       rearrange   as

 

y  = 2x + 5         (1)

 

And if L1 is parallel to L2, then, by the property of supplementary angles

 

5x + 2y - 25 + 2y + x + y    =  180       rearrange as

 

6x + 5y  =  205     (2)

 

Sub (1) into (2)

 

6x + 5 ( 2x + 5)   =  205

 

6x + 10x + 25   = 205

 

16x  =  180

 

x =  180 / 16   =   45/4   = 11.25

 

And 

 

y = 2 (11.25) + 5 =   27.5

 

 

cool cool cool

 Apr 11, 2022
 #4
avatar
0

Thank you so much!

Guest Apr 11, 2022

30 Online Users

avatar
avatar