Question

find the value of x.

Explanation:

Step1: Sum angles to 360° (full rotation)

The angles around point \(F\) include a right angle (\(90^\circ\)) and three \((x+4)^\circ\) angles, so:
$$(x+4) + (x+4) + (x+4) + 90 = 360$$

Step2: Simplify the left side

Combine like terms:
$$3(x+4) + 90 = 360$$

Step3: Isolate the term with \(x\)

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:
$$x = 90 - 4$$

Answer:

\(86\)