Final answer:
After setting up and solving the linear equation based on the angle bisector, the value of x is 5. Substituting x back into the expression for m∠ABE, the measure of angle ABE is found to be 17°, which does not match the provided options.
Step-by-step explanation:
The question involves solving a linear equation to find the measure of an angle. Since Ray BE bisects ∠ABC, we know that m∠ABE = m∠CBE. We can set up the equation (2x + 7)° = (5x − 8)° and solve for x. After solving for x, we find the value of m∠ABE by substituting x back into the expression (2x + 7)°.
Here is the step-by-step process:
- Set the equations equal to each other: (2x + 7)° = (5x – 8)°.
- Solve for x: 2x + 7 = 5x - 8 → 3x = 15 → x = 5.
- Find m∠ABE: m∠ABE = (2x + 7)° = (2(5) + 7)° = 17°.
The correct answer is m∠ABE = 17°, but this is not one of the options provided, indicating there may be a typo or misunderstanding in the question or answers given.
Simplifying this equation, we get 2x + 7 = 5x - 8.
Next, we can solve for x by subtracting 2x from both sides: 7 = 3x - 8.
Then, we add 8 to both sides: 15 = 3x.
Finally, divide both sides by 3 to solve for x: x = 5.
Now that we have the value of x, we can substitute it back into the equation to find the measure of angle ABE: (2x + 7)° = (2 * 5 + 7)° = 17°.