Question

question 12. after measuring the line segments, jane marked the congruent parts. if ad is 14 and ac is 4y - 32, use the markings to determine the value of y.

Explanation:

Step1: Identify congruent segments

From the markings, \(AD = DC\) and \(AE = EC\), so \(D\) is the midpoint of \(AC\). Thus, \(AC = 2\times AD\).

Step2: Substitute values and solve for y

Given \(AD = 14\) and \(AC = 4y - 32\), substitute into \(AC = 2\times AD\):
\(4y - 32 = 2\times14\)
\(4y - 32 = 28\)
Add 32 to both sides:
\(4y = 28 + 32\)
\(4y = 60\)
Divide both sides by 4:
\(y = \frac{60}{4}\)
\(y = 15\)

Answer:

\(y = 15\)