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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
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To find the value of x, we can set up an equation using the given angles:
Since the angles in the lower right corner are equal, we have:
5x + 15 = 1
Subtract 15 from both sides:
5x = -14
Divide by 5:
x = -14/5
Therefore, 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.
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.
The angle in the top right corner where the transversal intersects the bottom parallel line is (3x - 3) degrees.
Since the lines are parallel, corresponding angles are congruent. Therefore, we can set up the following equation:
3x - 3 = 5x + 15
Now, we can solve for x.
3x - 5x = 15 + 3
-2x = 18
x = 18 / -2
x = -9
Therefore, the value of x is -9.