Question

Attend to precision. Suppose that ∠1 and ∠2 are same-side interior angles formed by two parallel lines cut by a transversal, and that m∠1=7x-4 and m∠2=20x-5.
a.What is the value of x?

b.What is m∠1?

c.What is m∠2?

d.Explain how you found your answers.

Answer 1

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Answer:

  a)  x = 7

  b)  m∠1 = 45°

  c)  m∠2 = 135°

Step-by-step explanation:

a) Same-side interior angles are supplementary, so we have ...

  ∠1 +∠2 = 180

  (7x -4) +(20x -5) = 180

  27x = 189

  x = 7

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b) The measures of the angles can be found by substituting the value of x into the express for the angle measure.

  m∠1 = 7x -4 = 7(7) -4 = 45

  m∠1 = 45°

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c) Angle 2 is the supplement of angle 1, so ...

  m∠2 = 180° -45°

  m∠2 = 135°

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d) We used the relationship of angles at a transversal and the properties of equality.