Find the values of x and y. The lower left angle at the intersection of the transversal and upper parallel line is left parenthesis 3 y plus 5 right parenthesis degrees. The lower right angle at the intersection of the transversal and upper parallel line is left parenthesis 2 x plus 1 right parenthesis degrees. The upper left angle at the intersection of the transversal and lower parallel line is 85 degrees. (1 point) Responses
x = 42, y = 26.3
x = 42, y = 26.3
x = 47, y = 30
x = 47, y = 30
x = 42, y = 30
x = 42, y = 30
x = 47, y = 26.3
To find the values of x and y, we need to use the rules of parallel lines and transversals.
From the given information, we can set up the following equations:
Lower left angle + Lower right angle = 180 degrees (since they are corresponding angles)
Upper left angle + Lower left angle = 180 degrees (since they are alternate interior angles)
Upper left angle + Lower right angle = 180 degrees (since they are vertical angles)
Using the given values, we can substitute them into the equations:
(3y + 5) + (2x + 1) = 180
85 + (3y + 5) = 180
85 + (2x + 1) = 180
Simplifying each equation, we can solve for x and y:
3y + 2x + 6 = 180
3y + 90 = 180
2x + 86 = 180
Subtracting 6 from both sides of the first equation:
3y + 2x = 174
Subtracting 90 from both sides of the second equation:
3y = 90
Subtracting 86 from both sides of the third equation:
2x = 94
Dividing the second equation by 3:
y = 30
Dividing the third equation by 2:
x = 47
Therefore, the correct answer is:
x = 47, y = 30
To find the values of x and y, let's consider the properties of parallel lines and transversals.
1. The lower left angle at the intersection of the transversal and the upper parallel line is given as (3y + 5) degrees.
2. The lower right angle at the intersection of the transversal and the upper parallel line is given as (2x + 1) degrees.
3. The upper left angle at the intersection of the transversal and the lower parallel line is given as 85 degrees.
Now, let's analyze these given clues one by one.
1. The lower left angle at the intersection of the transversal and the upper parallel line is (3y + 5) degrees.
To find the value of y, we can equate this angle to 180 degrees (because the sum of angles in a triangle is 180 degrees) and solve for y:
3y + 5 = 180
3y = 180 - 5
3y = 175
y = 175/3
y ≈ 58.3
2. The lower right angle at the intersection of the transversal and the upper parallel line is (2x + 1) degrees.
To find the value of x, we can use the same approach as above:
2x + 1 = 180
2x = 180 - 1
2x = 179
x = 179/2
x ≈ 89.5
3. The upper left angle at the intersection of the transversal and the lower parallel line is 85 degrees.
This angle does not involve any variables, so it does not provide any additional information for finding x and y.
Therefore, the values of x and y are approximately x ≈ 89.5 and y ≈ 58.3.
The correct answer is x = 89.5, y ≈ 58.3.
To find the values of x and y, we need to use the properties of parallel lines and transversals and solve the system of equations.
Given:
- The lower left angle at the intersection of the transversal and upper parallel line is (3y + 5) degrees.
- The lower right angle at the intersection of the transversal and upper parallel line is (2x + 1) degrees.
- The upper left angle at the intersection of the transversal and lower parallel line is 85 degrees.
Let's set up the system of equations:
1) The sum of the lower left and lower right angles on the upper parallel line is equal to 180 degrees since they are corresponding angles:
(3y + 5) + (2x + 1) = 180
2) The sum of the upper left and lower left angles at the intersection of the transversal and lower parallel line is equal to 180 degrees since they are also corresponding angles:
(3y + 5) + 85 = 180
Now, we can solve this system of equations:
From equation 2:
3y + 5 + 85 = 180
3y + 90 = 180
3y = 180 - 90
3y = 90
y = 90 / 3
y = 30
Substitute y = 30 into equation 1 to find x:
(3y + 5) + (2x + 1) = 180
(3(30) + 5) + (2x + 1) = 180
(90 + 5) + (2x + 1) = 180
95 + 2x + 1 = 180
2x = 180 - 96
2x = 84
x = 84 / 2
x = 42
Therefore, the values of x and y are x = 42 and y = 30.
Answer: x = 42, y = 30.