Question

find the value of x.

Explanation:

Step1: Identify the triangle type

The triangle \( \triangle DEF \) is equilateral (all sides are equal). In an equilateral triangle, all angles are equal.

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \( 180^{\circ} \). Since all angles in an equilateral triangle are equal, if one angle is \( 6x^{\circ} \), then \( 6x+6x + 6x=180 \).
Simplify the left - hand side: \( 18x = 180 \).

Step3: Solve for \( x \)

Divide both sides of the equation \( 18x = 180 \) by \( 18 \): \( x=\frac{180}{18}=10 \).

Answer:

\( 10 \)