Question

find cd
b •———• c —————• d
2 2x - 6
blue arrow from b to d labeled x + 2
cd= box 16

Explanation:

Step1: Analyze the segment addition

From the diagram, \( BD = BC + CD \). We know \( BC = 2 \), \( CD = 2x - 6 \), and \( BD = x + 2 + 16\)? Wait, no, looking again, the blue arrow is \( x + 2 \) from B to D? Wait, maybe the total length \( BD \) can be expressed as \( BC + CD \), and also from the blue arrow, maybe \( BD = x + 2 + 16 \)? Wait, no, perhaps the total length is 16? Wait, maybe I misread. Wait, the diagram: B---C---D, with BC = 2, CD = 2x - 6, and the length from B to D is \( x + 2 \)? No, the blue arrow is from B to D with length \( x + 2 \), and there's a 16? Wait, maybe the total length \( BD = 16 \)? Wait, let's re-express.

Wait, the segment \( BD \) is composed of \( BC \) and \( CD \), so \( BD = BC + CD \). So \( BC = 2 \), \( CD = 2x - 6 \), so \( BD = 2 + (2x - 6) = 2x - 4 \). Also, from the blue arrow, maybe \( BD = x + 2 + 16 \)? No, that doesn't make sense. Wait, maybe the total length is 16, so \( BD = 16 \). Wait, the blue arrow is labeled \( x + 2 \), and then 16? Wait, maybe the diagram has \( BD = x + 2 + 16 \)? No, perhaps the correct equation is \( 2 + (2x - 6) = x + 2 + 16 \)? No, that seems off. Wait, maybe the length from B to D is 16, so \( BC + CD = 16 \). So \( 2 + (2x - 6) = 16 \). Let's solve that.

Step2: Solve for x

\( 2 + 2x - 6 = 16 \)
Simplify left side: \( 2x - 4 = 16 \)
Add 4 to both sides: \( 2x = 20 \)
Divide by 2: \( x = 10 \)

Step3: Find CD

Now, \( CD = 2x - 6 \). Substitute \( x = 10 \):
\( CD = 2(10) - 6 = 20 - 6 = 14 \)

Answer:

14