Ray BE bisects ∠ABC. If m∠ABE = (4x + 3)° and m∠CBE = (6x − 11)°, what is m∠ABE?
62°
49°
31°
7°
To find the measure of angle ABE, we need to set the two angle measurements equal to each other and solve for x.
4x + 3 = 6x - 11
Subtract 4x from both sides:
3 = 2x - 11
Add 11 to both sides:
14 = 2x
Divide both sides by 2:
x = 7
Now that we have the value of x, we can substitute it into either angle measurement to find the measure of angle ABE:
m∠ABE = 4x + 3 = 4(7) + 3 = 28 + 3 = 31°
Therefore, the measure of angle ABE is 31°. So the correct answer is 31°.