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ABD and CBD are adjacent given that m ABC is 68°. (m ABD = 2x + 5) and (m CBD = 3x + 8). Find CBD.

a) 30°
b) 34°
c) 38°
d) 42°

User Razor Jack
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1 Answer

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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°.

User Boosty
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