Question

find the value of x.
triangle xyz with angle at x is 60 degrees, side xz is labeled 3x + 8, side yz is labeled 4x - 4, and sides xz and xy are marked as equal (isosceles triangle).

Explanation:

Step1: Identify triangle type

The triangle has two equal sides (marked with ticks) and one angle of \(60^\circ\), so it's an equilateral triangle (all sides equal, all angles \(60^\circ\)). Thus, \(3x + 8 = 4x - 4\).

Step2: Solve for \(x\)

Subtract \(3x\) from both sides: \(8 = x - 4\).
Add 4 to both sides: \(x = 12\).

Answer:

\(x = 12\)