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In the diagram of a gate, the horizontal bars are parallel and the vertical bars are parallel. Find x and y.
Complete the explanation Indicating which postulates and/or theorems were used to find the values.

In The Diagram Of A Gate The Horizontal Bars Are Parallel And The Vertical Bars Are Parallel Find X And Y Complete The Explanation Indicating Which Postulates A class=

Sagot :

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Answer:

  • x = 6
  • y = 17
  • 18x +2y = 142 by the corresponding angles theorem, and
  • 3x +2y = 52 by the alternate interior angles theorem

Step-by-step explanation:

Given a set of parallel lines with a transversal and angles marked, you want to find the values for x and y consistent with the markings.

Setup

Alternate interior angles are congruent, so the marked acute angles have the same measure:

  3x +2y = 52

Corresponding angles are congruent, so the marked obtuse angles have the same measure:

  18x +2y = 142

Solution

Subtracting the first equation from the second gives ...

  (18x +2y) -(3x +2y) = (142) -(52)

  15x = 90

  x = 6

The value of y can be found from either equation. We choose to use the first:

  3(6) +2y = 52

  9 +y = 26 . . . . . . . . divide by 2

  y = 17 . . . . . . . . . subtract 9

Summary

  • x = 6
  • y = 17
  • 18x +2y = 142 by the corresponding angles theorem, and
  • 3x +2y = 52 by the alternate interior angles theorem

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