We are given that cos(x + 40) = 0.0872.
To find the value of x, we need to use the inverse cosine function, also known as arccosine or cos^-1.
Taking the inverse cosine of both sides, we get:
arccos(cos(x + 40)) = arccos(0.0872)
The inverse cosine and cosine functions are inverses of each other, so they "cancel out" on the left-hand side, leaving us with:
x + 40 = arccos(0.0872)
Using a calculator or a table of trigonometric values, we can find that arccos(0.0872) is approximately 84.74 degrees.
Subtracting 40 from both sides, we get:
x = 84.74 - 40
x = 44.74
So the value of x is approximately 44.74 degrees. None of the given options is an exact match, but the closest one is 45 degrees.