volume_mute
Refer to the below figure
publish date: 2024/03/01 01:47:00 UTC
volume_mute
If \(l_1 \parallel l_2 \) and m(∠3) = 120o, find the measures of the other seven angles that are labelled.
- m(∠1) =
- m(∠2) =
- m(∠4) =
- m(∠5) =
- m(∠6) =
- m(∠7) =
- m(∠8) =
Correct Answer
(1) 60
(2) 120
(3) 60
(4) 60
(5) 120
(6) 120
(7) 60
Explanation
- m(∠1) = 60o
- ∠3 and ∠1 are supplementary: m(∠3) + m(∠1) = 180o
- m(∠2) = 120o
- Vertical angles are congruent: m(∠2) = m(∠3)
- m(∠4) = 60o
- Vertical angles are congruent: m(∠4) = m(∠1)
- m(∠5) = 60o
- If two parallel lines are cut by a transversal, alternate interior angles are congruent: m(∠5) = m(∠4).
- m(∠6) = 120o
- If two parallel lines are cut by a transversal, alternate interior angles are congruent: m(∠6) = m(∠3).
- m(∠7) = 120o
- Vertical angles are congruent: m(∠7) = m(∠6)
- m(∠8) = 60o
- Vertical angles are congruent: m(∠8) = m(∠5)
Reference
Mathematics for college students