Question

Determine the value of x for which r ll s if:
m<1 = 40 - 4x; and
m<2 = 50 - 8x.

Answer 1

To find the value of x for which lines r and s are parallel given m<1 = 40 - 4x and m<2 = 50 - 8x, set the expressions equal to each other and solve for x to find that x = 2.5.

Step-by-step explanation:

To determine the value of x for which lines r is parallel to line s, we are given that the measure of angle 1 is m<1 = 40 - 4x, and the measure of angle 2 is m<2 = 50 - 8x. When two lines are parallel, the corresponding angles are equal, which means m<1 must be equal to m<2 for the lines to be parallel. We can set the two expressions that represent the measures of these angles equal to each other and solve for x:

40 - 4x = 50 - 8x

To solve this equation, we need to do some algebraic rearrangement:

1. Add 8x to both sides of the equation to bring all the x-terms to one side:
2. 
   
3. 
   
4. 40 - 4x + 8x = 50
5. 
   
6. 
   
7. Simplify the x-terms:
8. 
   
9. 
   
10. 40 + 4x = 50
11. 
    
12. 
    
13. Subtract 40 from both sides of the equation:
14. 
    
15. 
    
16. 4x = 10
17. 
    
18. 
    
19. Finally, divide both sides of the equation by 4 to solve for x:
20. 
    
21. 
    
22. x = 2.5

The value of x for which lines r and s are parallel is 2.5.