We are given the following diagram.
In this diagram, a line intersects the a and b. When two parallel lines are cut by a , special relationships exist. If we know the measure of one of the angles, we can find the measures of all of the angles. In this case, we know that m∠1 is 120∘. Therefore, we can use these relationships to find m∠2 and m∠3. Let's start by finding m∠2.
Notice that
∠1 and
∠2 are exterior angles that lie on opposite sides of the transversal. This means that
∠1 and
∠2 are . Since
a and
b are parallel, the measures of these angles are equal.
m∠2=m∠1=120∘
Next, we will find the measure of
∠3. To do so, let's take a closer look at
∠2 and
∠3.
We can see that
∠2 and
∠3 form a straight line, which means that
∠2 and
∠3 are . The measures of supplementary angles always add up to
180∘.
m∠2+m∠3=180∘
Since we know that
m∠2=120∘, we can find the measure of
∠3.
m∠2+m∠3=180
120+m∠3=180
m∠3=60
We found that
m∠2=120∘ and
m∠3=60∘.