Question

19,192 Learners found this answer helpful

a) create a segment addition equation to find the length of bc, then b) solve for x:
a ----22---- b ---------------- c
|-----------------------61-----------------------|

Explanation:

Part a)

Step1: Recall Segment Addition Postulate

The Segment Addition Postulate states that if \( B \) is between \( A \) and \( C \), then \( AB + BC = AC \). Let \( BC = x \). We know \( AB = 22 \) and \( AC = 61 \).

Step2: Write the equation

Substituting the known values into the postulate, we get \( 22 + x = 61 \).

Part b)

Step1: Solve for \( x \)

Start with the equation \( 22 + x = 61 \). Subtract 22 from both sides to isolate \( x \).
\[

$$\begin{align*} 22 + x - 22 &= 61 - 22\\ x &= 39 \end{align*}$$

\]

Answer:

s:
a) The Segment Addition equation is \( 22 + x = 61 \) (where \( x \) is the length of \( BC \)).
b) The value of \( x \) is \( \boldsymbol{39} \).