Question

line ef is a transversal through the parallel lines ab and cd. find the following measures if measure of angle 3 is 120 degrees and give the reason you know. a) what is measure of angle 5? i know m∠5 is degrees because m∠3 and m∠5 are angles and therefore. b) what is measure of angle 4? i know m∠4 is degrees because m∠3 and m∠4 are angles and therefore.

Explanation:

Step1: Identify angle - pair relationship for ∠3 and ∠5

∠3 and ∠5 are alternate interior angles. Since AB and CD are parallel lines and EF is a transversal, alternate interior angles are congruent.

Step2: Find the measure of ∠5

Given m∠3 = 120 degrees. Since ∠3 and ∠5 are alternate - interior angles and alternate interior angles are equal for parallel lines cut by a transversal, m∠5=120 degrees.

Step3: Identify angle - pair relationship for ∠3 and ∠4

∠3 and ∠4 are a linear pair. A linear pair of angles are supplementary, meaning their sum is 180 degrees.

Step4: Find the measure of ∠4

Let m∠4=x. We know that m∠3 + x=180 degrees. Given m∠3 = 120 degrees, then x = 180 - 120=60 degrees. So m∠4 = 60 degrees.

Answer:

a) m∠5 is 120 degrees because m∠3 and m∠5 are alternate interior angles and therefore equal for parallel lines AB and CD cut by transversal EF.
b) m∠4 is 60 degrees because m∠3 and m∠4 are a linear - pair angles and therefore supplementary.