We want to determine the value of x for the given measures of angles for which r∥ s.
In this case, we have been given expressions to represent the measures of ∠ 1 and ∠ 2.
m∠1&= 40-4x
m∠2&= 50-8x
Let's add these angle measures to the given figure so that we can get a better idea of their relationship.
If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel.
We can visualize this theorem. Consider two lines l and m. These lines are parallel if one of the following pairs of angles form a pair of corresponding congruent angles.
Applying the theorem, we can create an equation using the fact that the corresponding angles must be congruent for the lines r and s to be parallel.
(40-4x)^(∘)= (50-8x)^(∘)
Let's solve the equation for x.
Finally, we can use the fact that x=2.5 to determine the measures of ∠1 and ∠2.
m∠1&=40-4( 2.5)=30
m∠2&=50-8( 2.5)=30
For x=2.5 we have that r ∥ s, m ∠ 1 = 30, and m ∠ 2 = 30.
