Question

p is the point of concurrency for the angle bisectors of $\triangle abc$. find $m\angle bap$.
$m\angle bap = (4x)^\circ$
$m\angle cap = (6x - 20)^\circ$
$m\angle bap = ?^\circ$

Explanation:

Step1: Set angles equal (angle bisector)

Since \(P\) is the concurrency of angle bisectors, \(AP\) bisects \(\angle BAC\), so \(m\angle BAP = m\angle CAP\):
$$4x = 6x - 20$$

Step2: Solve for \(x\)

Rearrange to isolate \(x\):
$$20 = 6x - 4x \implies 20 = 2x \implies x = 10$$

Step3: Calculate \(m\angle BAP\)

Substitute \(x=10\) into \(4x\):
$$m\angle BAP = 4\times10$$

Answer:

\(40^\circ\)