Final answer:
The value of x that makes angle 2 equal to 2x+10 and angle 4 equal to 4x+80 is x = -35.
Step-by-step explanation:
To find the value of x that makes angle 2 equal to 2x+10 and angle 4 equal to 4x+80, we can set the two expressions equal to each other:
2x+10 = 4x+80
Now, we can solve for x by simplifying the equation:
2x - 4x = 80 - 10
-2x = 70
x = -70/2
x = -35
Therefore, the value of x that makes angle 2 equal to 2x+10 and angle 4 equal to 4x+80 is x = -35.