Question

what is the value of x? the value of x is (square^{circ}).

Explanation:

Step1: Identify triangle type

Since \(DE = EF\) (marked by the equal - side symbols), \(\triangle DEF\) is an isosceles triangle. In an isosceles triangle, the base - angles are equal, so \(\angle D=\angle F = x^{\circ}\).

Step2: Apply angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). So, in \(\triangle DEF\), we have \(\angle D+\angle F+\angle E=180^{\circ}\), which can be written as \(x + x+56 = 180\).
Combining like terms gives \(2x+56 = 180\).
Subtract 56 from both sides: \(2x=180 - 56\), so \(2x = 124\).
Divide both sides by 2: \(x=\frac{124}{2}=62\).

Answer:

\(62\)