Question

what is the value of x?

Explanation:

Step1: Use the Angle - Bisector Theorem (Angle Bisector is Equidistant from Sides)

Since \(SQ\) is the angle bisector of \(\angle RSP\) and \(SR\perp SS'\), \(SP\perp SS'\) (assuming the right - angle property from the figure's structure, where \(SQ\) is the bisector), we know that \(3x + 27=36\).

Step2: Solve the Equation for \(x\)

Subtract 27 from both sides of the equation \(3x+27 = 36\):
\(3x=36 - 27\)
\(3x = 9\)
Divide both sides by 3: \(x=\frac{9}{3}=3\)

Answer:

\(x = 3\)