Lines x and y are parallel. Write an equation that represents the relationship between b and e. Explain how you know this equation is always true. Your explanation should use AT LEAST TWO of the following terms: vertical angles, corresponding angles, congruent, supplementary.

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eudora eudora · Answer 1 · 2020-10-14T06:48:35+02:00

Answer:

m∠b + m∠e = 180°

Step-by-step explanation:

Lines x and y are the parallel lines and a transversal line is intersecting these lines.

∠b ≅ ∠h [Vertical angles]

∠h ≅ ∠f [Corresponding angles]

Therefore, ∠b ≅ ∠f [Congruent angles]

m∠f + m∠e = 180° [Supplementary angles]

m∠b + m∠e = 180° [Since, ∠b ≅ ∠f]

Therefore, equation representing the relation between ∠b and ∠e is,

m∠b + m∠e = 180°

abidemiokin abidemiokin · Answer 2 · 2021-11-16T10:17:19+01:00

The required equation that represents the relationship between b and e is m<b + m<e = 180

From the given diagram, we can see that the line x and y are cut by a transversal. This shows that the following statements are true;

m<b and m<g are supplementary i.e m<b + m<g = 180

Also m<b and m<f are equal (alternate interior angle)

m<b = m<d (vertically opposite angle)

Also, since m<d and m<e are supplementary angles (angle on a straight line), then m<b and m<e are also supplementary

Hence the required equation that represents the relationship between b and e is m<b + m<e = 180

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