Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Discover a wealth of knowledge from professionals across various disciplines on our user-friendly Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
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
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.