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Unit 3: Parallel Lines and Transversals

Homework 2: Parallel Lines Cut by a Transversal

Directions: If [tex] L \parallel m [/tex], solve for [tex] x [/tex] and [tex] y [/tex].

Answer :

If L // m, x = -15° and y = 85° when L // m.

When L // m, solve for x and y. Let L and M be parallel lines and t be the transversal. If L and m are parallel, then each pair of corresponding angles is congruent. Thus, we know that∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7 and ∠4 = ∠8. Additionally, we know that

∠1 + ∠2 + ∠3 = 180°,

since they form a straight line. Likewise,

∠5 + ∠6 + ∠7 = 180°,

since they form a straight line. We can use these facts to solve for x and y in the following steps:

∠1 + ∠2 + ∠3 = 180° 4x + 2y + 50° = 180° 4x + 2y = 130° (Equation 1)

∠5 + ∠6 + ∠7 = 180° 3x + 2y + 35° = 180° 3x + 2y = 145° (Equation 2)

We now have two equations in two variables. We can solve for one variable in terms of the other by solving

Equation 2 for y: 3x + 2y = 145° 2y = 145° - 3x y = (145° - 3x)/2

We can now substitute this expression for y into Equation 1:

4x + 2y = 130° 4x + 2[(145° - 3x)/2] = 130° 4x + 145° - 3x = 130° x + 145° = 130° x = -15°

Now that we have x, we can solve for y by substituting x = -15° into the expression for y:

y = (145° - 3x)/2 y = (145° - 3(-15°))/2 y = 85°

You can learn more about congruent at: brainly.com/question/30596171

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