Use properties of parallel lines cut by a transversal to find unknown angle measures

If two parallel lines are cut by a transversal, each pair of corresponding angles are congruent

If \(l_1 \parallel l_2\), then

• ∠ 1 ≅ 1($)
• ∠ 3 ≅ 2($)
• ∠ 2 ≅ 3($)
• ∠ 4 ≅ 4($)

If two parallel lines are cut by a transversal, alternate interior angles are congruent

if \(l_1 \parallel l_2 \) then

• ∠3 ≅ 1($)
• ∠4 ≅ 2($)

In the figure below, If \(l_1 \parallel l_2\) then

• ∠3 is supplementary to 1($)
• ∠4 is supplementary to 2($)

If \(l_1 \parallel l_2 \) and m(∠3) = 120^o, find the measures of the other seven angles that are labelled.

1. m(∠1) = 1($)
2. m(∠2) = 2($)
3. m(∠4) = 3($)
4. m(∠5) = 4($)
5. m(∠6) = 5($)
6. m(∠7) = 6($)
7. m(∠8) = 7($)

if \(\overline{AB} \parallel \overline{DE} \), which pairs of angles are congruent?

\(l_1 \parallel l_2 \).  Find \(x\)

\(x\) = 1($)

\(l_1 \parallel l_2\)

1. Find \(x\)
2. Find the measures of both angles labelled in the figure

\(x\) = 1($)

m(3x + 20^o) = 2($)

m(3x - 80^o) = 3($)