Question

1. find the value of x. (g6d)

Explanation:

Step1: Use the exterior angle property of an equilateral triangle

In an equilateral triangle, each interior angle is \(60^{\circ}\). The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Here, for the given triangle (which is equilateral as all interior angles are equal), the exterior angle \((8x + 40)^{\circ}\) and the adjacent interior angle form a linear pair. Also, using the exterior angle property (since the interior angles of the triangle are \(60^{\circ}\)), we can set up the equation \(8x+40 = 120\) (because the exterior angle of an equilateral triangle is \(120^{\circ}\) as \(180 - 60=120\)).

Step2: Solve the linear equation for \(x\)

Subtract \(40\) from both sides of the equation \(8x + 40=120\):
\(8x=120 - 40\)
\(8x = 80\)
Divide both sides by \(8\):
\(x=\frac{80}{8}\)

Answer:

\(x = 10\)