Question

find the value of x. (triangle def with all sides marked as equal, angle at f is 6x degrees)

Explanation:

Step1: Identify Triangle Type

The triangle \( \triangle DFE \) has all three sides marked as equal (indicated by the tick marks), so it is an equilateral triangle. In an equilateral triangle, all interior angles are equal and each angle measures \( 60^\circ \).

Step2: Set Up Equation

Since \( \angle F = 6x^\circ \) and in an equilateral triangle each angle is \( 60^\circ \), we set up the equation:
\( 6x = 60 \)

Step3: Solve for \( x \)

Divide both sides of the equation by 6:
\( x = \frac{60}{6} = 10 \)

Answer:

\( 10 \)