Final answer:
To find angle EBC, we calculate angles ABD and DBE from given equations and subtract their sum from 180 degrees. After solving for x, we find angle EBC, which should match one of the answer choices; however, in this case, a reevaluation of the information is necessary as the calculated result does not align with the provided options.
Step-by-step explanation:
To solve for angle EBC, we must understand that Ray BA and Ray BC are opposite rays, meaning angle ABC is a straight line and has a measure of 180°. Since Ray BE intersects angle DBC, creating two new angles, ABD and DBE, we can use these to find EBC. Given that angle ABD is 2x + 4 and angle DBE is 3x + 8, we can express angle EBC as the difference between 180° and the sum of angles ABD and DBE, shown by the equation 180 = (2x + 4) + (3x + 8) + angle EBC.
We can now solve for x:
- Combine like terms: 180 = 5x + 12 + angle EBC
- Subtract 12 from both sides: 168 = 5x + angle EBC
- Since angle ABD and angle DBE sum to 180° minus angle EBC, we find x by substituting the given angles back into our equation: 168 = (2x + 4) + (3x + 8)
- Simplify and solve for x: 168 = 5x + 12
- Subtract 12 from both sides: 156 = 5x
- Divide by 5: x = 31.2
Substitute x back into either angle ABD or DBE:
- Angle ABD = 2(31.2) + 4 = 66.4 + 4 = 70.4°
- Angle DBE = 3(31.2) + 8 = 93.6 + 8 = 101.6°
- Now calculate angle EBC: 180° - 70.4° - 101.6° = 8°
However, given our answer choices, it seems there's a possible error in the initial equation or the solution process - none of the answers match the calculated 8 degrees. We should recheck the calculations and possibly the input values for accuracy.