Question

find the value of x. x =

Explanation:

Step1: Set up the equation

The sum of angles around point \(F\) is \(90^{\circ}\) (right - angle) for the angles \((x + 4)^{\circ}\) (three times) and another \((x + 4)^{\circ}\). So, \(3(x + 4)+(x + 4)=90\).

Step2: Simplify the left - hand side

Using the distributive property \(a(b + c)=ab+ac\), we have \((3x+12)+(x + 4)=90\). Combine like terms: \(3x+x+12 + 4=90\), which simplifies to \(4x+16 = 90\).

Step3: Solve for \(x\)

Subtract \(16\) from both sides: \(4x+16-16=90 - 16\), so \(4x=74\). Then divide both sides by \(4\): \(x=\frac{74}{4}=18.5\).

Answer:

\(18.5\)