Suppose the traffic light is hung so that the tensions T1 and T2 are both equal to 80 N. Find the new angles they make with respect to the x-axis. (By symmetry, these angles will be the same.)

To find the angles made by tensions T1 and T2 with respect to the x-axis, we can use the concept of trigonometry.

First, let's draw a diagram to visualize the problem. Assuming that the traffic light is hanging vertically downward, we have the following setup:

|
|
T2 |
<-------+
|
|
T1 |
<-------+
|
|
|
--------+--------
x-axis

In this diagram, T1 and T2 represent the tensions acting on the traffic light. By symmetry, the angles between these tensions and the x-axis will be the same.

Now, let's break down the tensions T1 and T2 into their x and y components. Since the traffic light is hanging vertically downward, T1 and T2 only have y-components. Considering that T1 and T2 are equal (both 80 N), we have:

T1y = T2y = 80 N

Next, we need to find the values of T1y and T2y in order to calculate the angles they make with respect to the x-axis. To do this, we can use trigonometry.

By applying the concept of right triangles, we can see that T1y and T2y are the opposite sides, and the hypotenuse is the tension (80 N). The adjacent side is 0 because there is no force acting in the x-direction.

Applying the trigonometric function tangent (tan), we can write the equations:

tan(theta) = T1y / 0
tan(theta) = T2y / 0

Since the adjacent side is 0 in both cases, the tangent is undefined. This means that the angles made by T1 and T2 with respect to the x-axis are both 90 degrees (or pi/2 radians).

Therefore, the new angles made by tensions T1 and T2 with respect to the x-axis are both 90 degrees (or pi/2 radians).