Question

applying the converse of the isosceles triangle theorem
try it
consider isosceles δxyz.
what is the value of n?
what is the measure of leg xy? ft
what is the measure of leg xz? ft
(9n + 12) ft
x (15n − 6) ft z

Explanation:

Step1: Identify equal sides

In isosceles ΔXYZ, the marked angles at Y and Z imply XY = XZ. So, $9n + 12 = 15n - 6$.

Step2: Solve for n

Rearrange the equation: $12 + 6 = 15n - 9n$ → $18 = 6n$ → $n = 3$.

Step3: Calculate XY

Substitute n=3 into XY: $9(3) + 12 = 27 + 12 = 39$.

Step4: Calculate XZ

Substitute n=3 into XZ: $15(3) - 6 = 45 - 6 = 39$.

Answer:

n = 3
Measure of leg XY = 39 ft
Measure of leg XZ = 39 ft