Question

p is the point of concurrency for the angle bisectors of $\triangle abc$. find $m\angle bcp$.
$m\angle bcp = (6x)^\circ$
$m\angle acp = (4x + 6)^\circ$
$m\angle bcp = ?^\circ$

Explanation:

Step1: Set angles equal (angle bisector)

Since \(P\) is the concurrency of angle bisectors, \(CP\) bisects \(\angle ACB\), so \(m\angle BCP = m\angle ACP\).
\(6x = 4x + 6\)

Step2: Solve for \(x\)

Subtract \(4x\) from both sides.
\(6x - 4x = 6 \implies 2x = 6 \implies x = 3\)

Step3: Calculate \(m\angle BCP\)

Substitute \(x=3\) into \(6x\).
\(m\angle BCP = 6 \times 3\)

Answer:

\(18^\circ\)