Question

9.
60°
7x + 19
11x - 89
60°

Explanation:

Step1: Recognize the triangle type

Since two angles are \(60^{\circ}\), the triangle is equilateral. In an equilateral triangle, all sides are equal. So, \(7x + 19=11x - 89\).

Step2: Solve the equation for \(x\)

Subtract \(7x\) from both sides: \(19 = 4x-89\).
Add \(89\) to both sides: \(19 + 89=4x\), so \(108 = 4x\).
Divide both sides by \(4\): \(x=\frac{108}{4}=27\).

Answer:

\(x = 27\)