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 value of x and then substitute it into the expression for m∠ABE, we set the two expressions for m∠ABE and m∠CBE equal to each other:
4x + 3 = 6x - 11
Subtract 4x from both sides:
3 = 2x - 11
Add 11 to both sides:
14 = 2x
Divide both sides by 2:
7 = x
Now we substitute this value of x into the expression for m∠ABE:
m∠ABE = 4x + 3 = 4(7) + 3 = 28 + 3 = 31
Therefore, m∠ABE = 31°.