Question

1. write and use an equation to find the value of x that makes the segment addition theorem true.

b • 11 c • 2x + 29 d

29 + x

x =

Explanation:

Step1: Apply Segment Addition Theorem

According to the Segment Addition Theorem, \(BC + CD=BD\). So, \(11+(2x + 29)=29 + x\).

Step2: Simplify the left - hand side

Combine like terms on the left - hand side: \(11+2x+29=2x + 40\). So the equation becomes \(2x+40=29 + x\).

Step3: Isolate the variable x

Subtract \(x\) from both sides of the equation: \(2x - x+40=29+x - x\), which simplifies to \(x + 40=29\).

Step4: Solve for x

Subtract 40 from both sides: \(x=29 - 40\).

Answer:

\(x=-11\)