4 of 54 of 5 Items
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
24
24
9
9
21
21
14
14
Skip to navigation
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
24
24
9
9
21
21
14
14
Skip to navigation
To find the value of x, we can set up an equation using the given information.
From the diagram, we know that the angle in the lower right corner where the transversal intersects the top parallel line is 5x + 15 degrees, and the angle in the lower right corner where the transversal intersects the bottom parallel line is 1 degree.
Since these angles are corresponding angles (they are on the same side of the transversal and in corresponding positions), they must be congruent.
Therefore, we can set up the equation:
5x + 15 = 1
Simplifying this equation, we get:
5x = 1 - 15
5x = -14
Dividing both sides of the equation by 5, we find:
x = -14/5
So, the value of x is -14/5 or -2.8.
To find the value of x, we can set up an equation using the given angles.
According to the diagram, the angle in the lower right corner where the transversal intersects the top parallel line is given as 5x + 15 degrees.
The angle in the lower right corner where the transversal intersects the bottom parallel line is given as 1 degree.
To find x, we need to equate these two angles.
5x + 15 = 1
Now, we can solve for x:
5x = 1 - 15
5x = -14
x = -14/5
x = -2.8
Therefore, the value of x is -2.8.