Question

1. find the value of x.

3x + 8
60°
4x - 4

Explanation:

Step1: Identify the triangle type

Since two sides are marked equal, it is an isosceles triangle. In an isosceles triangle, the sides opposite equal angles are equal. Here, the angle is \(60^{\circ}\), so it is an equilateral triangle (all angles \(60^{\circ}\) in an equilateral triangle, and all sides equal).

Step2: Set up the equation

Set \(3x + 8=4x - 4\) (because in an equilateral triangle \(ZX = XY\)).

Step3: Solve for \(x\)

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

Answer:

\(x = 12\)