Answer:
[tex]x=12[/tex]
Step-by-step explanation:
We know that [tex]\ell\parallel m[/tex].
Then by the properties of a transversal cutting a pair of parallel lines, we can write:
[tex](9x-4)+(5x+16)=180[/tex]
The property used here is the Consecutive Angles Property. The two consecutive angles are supplementary.
Now, we can solve for x. Rearrange:
[tex](9x+5x)+(-4+16)=180[/tex]
Combine like terms:
[tex]14x+12=180[/tex]
Subtract 12 from both sides:
[tex]14x=168[/tex]
Divide both sides by 14:
[tex]x=12[/tex]
So, the value of x is 12.
