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

User Ethanolle
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1 Answer

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Final answer:

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. 40 - 4x + 8x = 50


  3. Simplify the x-terms:


  4. 40 + 4x = 50


  5. Subtract 40 from both sides of the equation:


  6. 4x = 10


  7. Finally, divide both sides of the equation by 4 to solve for x:


  8. x = 2.5



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

User Tal Zion
by
8.1k points

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