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&= 60-2x
m∠2&= 70-4x
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.
(60-2x)^(∘)= (70-4x)^(∘)
Let's solve the equation for x.
Finally, we can use the fact that x=5 to determine the measures of ∠1 and ∠2.
m∠1&=60-2( 5)=50
m∠2&=70-4( 5)=50
For x=5 we have that r ∥ s, m ∠ 1 = 50, and m ∠ 2 = 50.
