Use the diagram below to answer questions 4–5. 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 measure of 1? (1 point) Responses 45o 45 o 60o 60 o 120o 120 o 125o 125 o

Question

Use the diagram below to answer questions 4–5. 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 measure of 1? (1 point) Responses 45o 45 o 60o 60 o 120o 120 o 125o 125 o

Answer 1

The measure of angle 1 is 120o.

Answer 2

To find the measure of angle 1, we need to use the fact that corresponding angles formed by a transversal and parallel lines are congruent.

Angle 1 is corresponding to the angle in the lower right of the top parallel line, which is marked as (5x + 15) degrees.

Therefore, we can set up the equation:

1 = 5x + 15

To solve for x, we can subtract 15 from both sides:

1 - 15 = 5x

-14 = 5x

Then divide both sides by 5:

-14/5 = x

x = -2.8

Now that we have found the value of x, we can substitute it back into the expression for angle 1:

1 = 5(-2.8) + 15

1 = -14 + 15

1 = 1

So, the measure of angle 1 is indeed 1 degree.

Answer 3

To determine the measure of angle 1, we need to use the properties of parallel lines and transversals.

Looking at the diagram, we see that angle 1 is formed by the intersection of the bottom parallel line and the transversal. We are told that the angle in the lower right corner of this intersection is marked as "1".

Since the bottom parallel line and the top parallel line are parallel, the angles formed by the transversal are corresponding angles. Corresponding angles that are formed by a transversal and parallel lines are congruent, meaning they have the same measure.

Therefore, angle 1 is congruent to the angle in the lower right corner of the intersection of the top parallel line and the transversal, which is marked as "1".

So, the measure of angle 1 is the same as the measure of angle 1 in the lower right corner, which is 1 according to the diagram.