Final answer:
To find x, simplify and solve the equation 5x + 12 + 9x + 1 + 10x - 37 = 180. The value of x is 9. The measure of the exterior angle at point A is 57 degrees.
Step-by-step explanation:
To find the value of x, we need to set up an equation using the given information. The sum of the interior angles of a triangle is always equal to 180 degrees. So, the equation would be: 5x + 12 + 9x + 1 + 10x - 37 = 180.
Simplifying the equation, we get: 24x - 24 = 180. Solving for x, we find that x = 9.
The measure of an exterior angle at point A is equal to the sum of the remote interior angles. So, the exterior angle would be: 5x + 12 = 5(9) + 12 = 57 degrees.