Question

qc is the angle bisector of △abc. find the value of x.

Explanation:

Step1: Use the Angle Bisector Theorem

Since \(QC\) is the angle bisector of \(\angle ACB\) and \(QC\perp AB\) (right - angle at \(Q\)) and \(AC = BC\) (marked as equal), then \(\angle ACQ=\angle BCQ\). So, \(3x + 7=4x-8\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides of the equation \(3x + 7=4x-8\):
\(3x-3x + 7=4x-3x-8\)
\(7=x - 8\).
Then add \(8\) to both sides:
\(x=7 + 8\).

Answer:

\(x = 15\)