Question

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.

Answer 1

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

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