To determine the measure of angle $A$ so that the braces of the bridge remain parallel, we can follow these steps:

Step-by-Step Solution

1. Identify the Properties of Parallel Lines and Triangles: Since the top and bottom structures of the bridge are parallel, the interior angles of each triangular section must add up to 180°, ensuring that angle $A$ aligns with the parallel lines property.

2. Set Up the Equation for Angles: The three angles in the triangular section (where angle $A$ is located) are given as follows:

   • One angle is labeled $7x - 5$,
   • Another angle is labeled $2x + 45$,
   • The third angle is angle $A$.

   Since these are the angles of a triangle, their sum must equal 180°: $(7x - 5) + (2x + 45) + A = 180$

3. Simplify and Solve for $x$: Combine the terms involving $x$: $9x + 40 + A = 180$ Rearranging, we find: $9x + A = 140$

4. Substitute and Check Options: We need the value of angle $A$ for the braces to remain parallel. This would depend on solving for $x$ and substituting back.

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