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Refer to the below figure

publish date: 2024/03/01 01:47:00 UTC

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

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

(1) 60

(2) 120

(3) 60

(4) 60

(5) 120

(6) 120

(7) 60

m(∠1) = 60^o
- ∠3 and ∠1 are supplementary: m(∠3) + m(∠1) = 180^o
m(∠2) = 120^o
- Vertical angles are congruent: m(∠2) = m(∠3)
m(∠4) = 60^o
- Vertical angles are congruent: m(∠4) = m(∠1)
m(∠5) = 60^o
- If two parallel lines are cut by a transversal, alternate interior angles are congruent: m(∠5) = m(∠4).
m(∠6) = 120^o
- If two parallel lines are cut by a transversal, alternate interior angles are congruent: m(∠6) = m(∠3).
m(∠7) = 120^o
- Vertical angles are congruent: m(∠7) = m(∠6)
m(∠8) = 60^o
- Vertical angles are congruent: m(∠8) = m(∠5)

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