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&= 80-x
m∠2&= 90-2x
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.
(80-x)^(∘)= (90-2x)^(∘)
Let's solve the equation for x.
Finally, we can use the fact that x=10 to determine the measures of ∠1 and ∠2.
m∠1&=80- 10=70
m∠2&=90-2( 10)=70
For x=10 we have that r ∥ s, m ∠1 = 70, and m ∠2 = 70.
