Start with ∠2 and ∠3 and isolate the lines and transversal we need.
m∠1=47^(∘)
m∠2=133^(∘)
m∠3=47^(∘)
Practice makes perfect
Let's start with ∠2 and ∠3 and isolate the lines and transversal we need.
The known angle, 133^(∘), and ∠2 are between the lines, but on opposite sides of the transversal. We can therefore classify them as alternate interior angles. According to the Alternate Interior Angles Theorem, they are congruent if the lines are parallel. Since the lines are parallel, we have that
m∠2=133^(∘).When it comes to ∠3, this angle is also between the lines but on the same side of the transversal. We can therefore classify them as consecutive interior angles. According to the Consecutive Interior Angles Theorem, they are supplementary if the lines are parallel. Now we can write an equation
m∠3+133=180.
Let's solve this equation for m∠3.
When we know m∠2 and m∠3, we can classify m∠1 using either one of the angles. Let's use m∠2 and isolate the lines and transversal we need.
Since both angles are between the sides and to the left of the transveral, they are consecutive interior angles and therefore supplementary if the lines are parallel. The lines are parallel so we can write the equation
m∠1+133=180.
Let's solve this equation for m∠1.
