Question

p is the point of concurrency for the angle bisectors of $\triangle abc$. find $m\angle acp$.
$m\angle bcp = (4x + 1)^\circ$
$m\angle acp = (5x - 5)^\circ$
$m\angle acp = ?^\circ$

Explanation:

Step1: Set angles equal (angle bisector)

Since \(P\) is the concurrency point of angle bisectors, \(CP\) bisects \(\angle ACB\), so \(m\angle BCP = m\angle ACP\).
$$4x + 1 = 5x - 5$$

Step2: Solve for \(x\)

Rearrange to isolate \(x\):
$$1 + 5 = 5x - 4x$$
$$x = 6$$

Step3: Substitute \(x\) into \(m\angle ACP\)

Use the expression for \(m\angle ACP\):
$$m\angle ACP = 5(6) - 5$$

Answer:

\(25^\circ\)