Question

part 3 - in the figure ba and bc are opposite rays, and ∠abf is bisected by be.

1. if m∠abe = 2n + 7 and m∠ebf = 4n - 11, find m∠abe.

Explanation:

Step1: Use the angle - bisector property

Since \(BE\) bisects \(\angle ABF\), then \(m\angle ABE=m\angle EBF\).
So, \(2n + 7=4n-11\).

Step2: Solve the equation for \(n\)

Subtract \(2n\) from both sides:
\(2n+7 - 2n=4n - 11-2n\)
\(7 = 2n-11\).
Add \(11\) to both sides:
\(7 + 11=2n-11 + 11\)
\(18=2n\).
Divide both sides by \(2\):
\(n=\frac{18}{2}=9\).

Step3: Find \(m\angle ABE\)

Substitute \(n = 9\) into the expression for \(m\angle ABE\) (\(m\angle ABE=2n + 7\)).
\(m\angle ABE=2\times9+7\)
\(m\angle ABE=18 + 7\)
\(m\angle ABE=25\).

Answer:

\(25\)