Question

find the value of x.
(there is a diagram with point f, rays fb (left), fc (down-left), fd (down), fe (down-right). angles: ∠bfc = (x + 4)°, ∠cfd = (x + 4)°, ∠dfe = (x + 4)°, and ∠bfe is a right angle (90°? wait, no, looking at the diagram, maybe ∠bfe is a right angle? wait, the diagram shows fb horizontal left, fe vertical down? wait, the angles at f: ∠bfc, ∠cfd, ∠dfe each (x + 4)°, and maybe ∠bfe is 90°? wait, no, maybe the total angle around f for those angles sums to 90°? wait, the users diagram: fb is left, fc is a ray down-left, fd down, fe down-right. so the angles between fb and fe: ∠bfc, ∠cfd, ∠dfe. wait, maybe ∠bfe is a right angle (90°), so the sum of ∠bfc + ∠cfd + ∠dfe = 90°? wait, each angle is (x + 4)°, so 3*(x + 4) = 90? wait, but the diagram has a right angle symbol at f between fb and fe? wait, the original problems diagram: at point f, fb is left, fe is down, and theres a right angle symbol between fb and fe? so ∠bfe is 90°, and the three angles ∠bfc, ∠cfd, ∠dfe each (x + 4)°, so their sum is 90°. so 3(x + 4) = 90? wait, but maybe i misread. alternatively, maybe ∠bfc and ∠cfe? wait, no, the ocr text is: \find the value of x.\ with the diagram as described. so the ocr text is the problem statement plus the diagram description. so the ocr text is: \find the value of x.\ (and the diagram details as above).

Explanation:

Step1: Sum angles to full rotation

The total around point $F$ is $360^\circ$, including a right angle.
$$(x+4)^\circ + (x+4)^\circ + (x+4)^\circ + 90^\circ = 360^\circ$$

Step2: Simplify the left side

Combine like terms for the angles.
$$3(x+4) + 90 = 360$$

Step3: Isolate the variable term

Subtract 90 from both sides.
$$3(x+4) = 360 - 90$$
$$3(x+4) = 270$$

Step4: Solve for $(x+4)$

Divide both sides by 3.
$$x+4 = \frac{270}{3}$$
$$x+4 = 90$$

Step5: Solve for $x$

Subtract 4 from both sides.
$$x = 90 - 4$$
$$x = 86$$

Answer:

$86$