Question

find the value of x.
diagram: horizontal line ab with f at center. from f, downward to d, left - downward to e, right - downward to c. angles ∠afe, ∠efd, ∠dfc, ∠cfb are each labeled ((x - 2)^circ). below: (x=square)

Explanation:

Answer:

To find the value of \( x \), we note that the sum of the angles around a straight line (which is \( 180^\circ \)) is equal to the sum of the four angles given, each of measure \( (x - 2)^\circ \).

So we set up the equation:
\[
4(x - 2) = 180
\]

First, divide both sides by 4:
\[
x - 2 = \frac{180}{4} = 45
\]

Then, add 2 to both sides:
\[
x = 45 + 2 = 47
\]

So the value of \( x \) is \( \boxed{47} \).