Question

Ray BE bisects ∠ABC. If m∠ABE = (2x + 7)° and m∠CBE = (5x − 8)°, what is m∠ABE?

5°
17°
33°
34°

Answer 1

Since ray BE bisects angle ABC, we have:

\[
m\angle ABE = m\angle CBE
\]

According to the problem, we have:

\[
m\angle ABE = (2x + 7)^\circ
\]
\[
m\angle CBE = (5x - 8)^\circ
\]

Setting the two expressions equal to each other gives us:

\[
2x + 7 = 5x - 8
\]

Now, we solve for \(x\):

1. Subtract \(2x\) from both sides:

\[
7 = 3x - 8
\]

2. Add \(8\) to both sides:

\[
15 = 3x
\]

3. Divide by \(3\):

\[
x = 5
\]

Now we substitute \(x\) back into the expression for \(m\angle ABE\):

\[
m\angle ABE = 2(5) + 7 = 10 + 7 = 17^\circ
\]

Thus, the measure of \(m\angle ABE\) is:

\[
\boxed{17}
\]