Question

determine the value of ( x ) in the isosceles triangle.

enter the answer in the space provided. use numbers instead of words.

( x = square )

Explanation:

Step1: Identify triangle properties

In isosceles triangle \(ABC\), \(AC = BC = 8\) in. \(CD\) is perpendicular to \(AB\), so \(CD\) is the angle - bisector (by the property of isosceles triangles: the altitude from the vertex angle of an isosceles triangle bisects the vertex angle).

Step2: Determine the value of \(x\)

Since \(CD\) bisects \(\angle ACB\), and one part of the bisected angle is \(32^{\circ}\), the other part \(x\) is also \(32^{\circ}\) (because the angle - bisector divides the vertex angle into two equal angles).

Answer:

\(32\)