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

9514 1404 393

Answer:

a) x = 7

b) m∠1 = 45°

c) m∠2 = 135°

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.