Question

Find the values of x and y. State which theorem(s) you used. 1. 2. 3 . 3x + 23) 30° 5x 45 y 4x Ly - 4). (3x + 501 y +12) 4. When two parallel lines are cut by a transversal, name the angles that are congruent. I 5.When two parallel lines are cut by a transversal, name the angles that are supplementary Find the value of x that makes line min. 6. 7 8. n 5x m 3x + 47) G+ m (2x + 78) Write the equation of the line that passes through the given point and is parallel to the given tine. 9. (-3, --4): y = 3x - 8 10. (3,6); 2x - 6y = 12

Answer 1

To find the values of x and y, we can set up equations using properties of parallel lines and transversals. By solving these equations, we find that x = 1 and y = 50.

Step-by-step explanation:

To find the values of x and y, we can use the given information about parallel lines and transversals. From the information given in the question, we can set up some equations and use properties of parallel lines and transversals to solve for the values of x and y. Let's go step by step:

1. Using the given information about parallel lines and transversals, we can write the equation (3x + 23) + (y - 4) = 180, since the sum of the angles on the same side of a transversal is 180 degrees.
2. Expanding the equation, we have 3x + y - 4 + 23 = 180.
3. Simplifying the equation, we get 3x + y + 19 = 180.
4. Now, we can use the information given in the question to solve for x and y. We have 5x + 45 = 3x + 47.
5. Subtracting 3x from both sides, we get 2x + 45 = 47.
6. Subtracting 45 from both sides, we get 2x = 2.
7. Dividing both sides by 2, we get x = 1.
8. Substituting x = 1 into the equation 5x + 45 = 3x + 47, we get 5(1) + 45 = 3(1) + 47.
9. Simplifying the equation, we get 5 + 45 = 3 + 47.
10. Adding the numbers, we get 50 = 50.
11. Therefore, x = 1 and y = 50.