Question

stayed bridge is similar to a suspension bridge, but is more efficient for medium distances. In this design of bridge, there are two towers, and strong cables attach to the tops of the towers and the sides of the bridge. Assume the bridge is perpendicular to the two towers. a. Angle A is 35 degrees. Explain how you can find the measure of angles B, C, and D. (Hint: all angles in a triangle add to 180 degrees.) Can you find the measure of every angle on the bridge

1. The measure of every angle on the bridge is:
A = 35°
B = 55°
C = 55°
D = 55°
Given,
The bridge is perpendicular to the two towers.
Angle A is 35°
We have to find that the measure of angles B, C, and D.
So, For this purpose, we know that the
Angle A is 35° and hint given is that the all angles in a triangle add to 180°
So,
A + B + X = 180°
We know that A = 35° and X = 90° and
35° + B + 90° = 180°
B = 180° – 90° – 35°
B = 55°
And
Now we find that the another angle Y.
So,
A + B + Y = 180°
35° + 55° + Y = 180°
Y = 90°
Then
In order to calculate C, you have to make an assumption that was not given in the problem. The assumption is that triangles ABX and YCZ are mirror images of each other.
Then,
B = C = 55°
And
also since they are similar triangles,
D = C = 55°.
So, the measure of every angle on the bridge is:
A = 35°
B = 55°
C = 55°
D = 55°