Question

7x + 19
60°
60°
11x - 89

Explanation:

Step1: Determine the type of triangle

Since two angles are \(60^{\circ}\), the third angle is \(180^{\circ}-60^{\circ}-60^{\circ} = 60^{\circ}\). So, it is an equilateral triangle.

Step2: Set up the equation

In an equilateral triangle, all sides are equal. So, \(7x + 19=11x-89\).

Step3: Solve the equation

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

Answer:

\(x = 27\)