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Use the theorems of parallel lines to solve for x in the following.

 

 Mar 11, 2021
 #1
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These lines are parallel, so once we draw a line through both of them those to angles are the same

 

9x+24=x^2+4x

x^2-5x-24=0

we see that -8 and 3 are the roots as they add up to -5 and multiply to -24

there fore (x+8)(x-3)=0

however we notice when we plug in negative eight. The second angle gives a negative value, so therefore 3 is the answer


$\boxed{3}$

 Mar 11, 2021
 #2
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Wrong way around answer is $\boxed{8}$ =

 Mar 11, 2021
 #3
avatar+118069 
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The parallel lines cut by the transversal form consecutive (equal)  angles....so...

 

x^2 + 4x  =  9x + 24     rearrange  as

 

x^2  -  5x   -  24    = 0         factor

 

(x - 8) ( x + 3)   =  0

 

The first  factor gives us what we need

 

x  - 8   =  0

 

x  = 8

 

 

cool cool cool

 Mar 11, 2021

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