Question

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

Explanation:

Step1: Analyze the segment addition

From the diagram, \( BC + CD = BD \), and \( BD = x + 2 \), \( BC = 2 \), \( CD = 2x - 6 \). So we have the equation \( 2+(2x - 6)=x + 2 \).

Step2: Solve for x

Simplify the left - hand side of the equation: \( 2+2x - 6=2x - 4 \). So the equation becomes \( 2x - 4=x + 2 \).
Subtract \( x \) from both sides: \( 2x - x-4=x - x + 2 \), which gives \( x - 4 = 2 \).
Add 4 to both sides: \( x-4 + 4=2 + 4 \), so \( x = 6 \).

Step3: Find the length of CD

Since \( CD = 2x - 6 \), substitute \( x = 6 \) into the expression: \( CD=2\times6 - 6 \).
First, calculate \( 2\times6 = 12 \), then \( 12-6 = 6 \).

Answer:

\( 6 \)