Final answer:
To find CBD, set up an equation using the given information and solve for x. Then substitute the value of x into the equation to find the measure of CBD.
Step-by-step explanation:
To find CBD, we need to set up an equation using the given information. Since ABD and CBD are adjacent angles, they share a common side and vertex, which is angle ABC. We know that m(ABC) is 68°, and m(ABD) is 2x + 5, and m(CBD) is 3x + 8.
Using the fact that the sum of adjacent angles is equal to the measure of the angle formed, we can set up an equation: (2x + 5) + (3x + 8) = 68.
Simplifying the equation, we get 5x + 13 = 68. Solving for x, we find x = 11.
Now, we can find the measure of CBD by substituting the value of x back into the equation: m(CBD) = 3(11) + 8 = 33 + 8 = 41°.