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 know that:

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

Given the expressions for the angles:

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

Setting these two expressions equal:

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

Now, we can 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 can find \( m\angle ABE \):

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

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

\[
\boxed{17^\circ}
\]