Feature
Use the diagram below to answer questions 4–5.
Alt: Two horizontal, parallel lines are cut by a transversal. Where the transversal intersects the top parallel line, the angle in the lower right corner is labeled left parenthesis 5 x plus 15 right parenthesis degrees. Where the transversal intersects the bottom parallel line, the angle in the top right corner is labeled left parenthesis 3 x minus 3 right parenthesis degrees. Where the transversal intersects the bottom parallel line, the angle in the bottom right corner is labeled 1.The transversal goes from the lower left to the upper right. Arrows on the parallel lines indicate that they are parallel. The intersection of the bottom parallel line with the transversal creates 4 angles. The angle in the upper right is marked left parenthesis 3 x minus 3 right parenthesis degrees. The angle in the lower right is marked 1. The intersection of the top parallel line with the transversal creates 4 angles. The angle in the lower right is marked left parenthesis 5 x plus 15 right parenthesis degrees.
Question
What is the value of x?
(1 point)
Responses
A. 24
B. 9
C. 21
D. 14
To find the value of x, we can set up an equation based on the given information.
The angle in the lower right corner where the transversal intersects the top parallel line is labeled (5x + 15) degrees.
The angle in the top right corner where the transversal intersects the bottom parallel line is labeled (3x - 3) degrees.
Since the angles on a straight line add up to 180 degrees, we can set up the equation:
(5x + 15) + (3x - 3) = 180
Combining like terms:
8x + 12 = 180
Subtracting 12 from both sides:
8x = 168
Dividing both sides by 8:
x = 21
Therefore, the value of x is 21.
Answer: C. 21
To find the value of x, we can set up an equation by equating the two corresponding angles formed by the transversal and the parallel lines.
The angle in the lower right corner formed by the transversal and the top parallel line is labeled (5x + 15) degrees.
The angle in the top right corner formed by the transversal and the bottom parallel line is labeled (3x - 3) degrees.
Therefore, we have the equation: 5x + 15 = 3x - 3
To solve the equation, we can subtract 3x from both sides and subtract 15 from both sides:
5x + 15 - 3x = 3x - 3 - 3x
2x + 15 = -3
Subtracting 15 from both sides:
2x + 15 - 15 = -3 - 15
2x = -18
Finally, dividing both sides by 2, we get:
x = -18/2
Therefore, the value of x is -9.
So, the correct answer is:
B. 9