Question

if ( mangle cdb = 3x - 23 ), what is the value of ( x )?

Explanation:

Step1: Analyze the angle

Since \(CD\perp AB\), \(\angle CDB = 90^{\circ}\).

Step2: Set up the equation

Given \(m\angle CDB=3x - 23\), and \(m\angle CDB = 90^{\circ}\), we have the equation \(3x-23 = 90\).

Step3: Solve for \(x\)

Add \(23\) to both sides: \(3x=90 + 23\), so \(3x=113\).
Divide both sides by \(3\): \(x=\frac{113}{3}\approx37.67\).

Answer:

\(x=\frac{113}{3}\)