Question

what is the value of x?
the value of x is □°.

Explanation:

Step1: Identify the triangle type

The triangle \( \triangle DEF \) is isosceles (\( DE = EF \)), so \( \angle D=\angle F=x \).

Step2: Use the triangle - angle - sum theorem

The sum of angles in a triangle is \( 180^{\circ} \). So \( \angle D+\angle F+\angle E = 180^{\circ} \). Substitute \( \angle D = x \), \( \angle F=x \), and \( \angle E = 28^{\circ} \) into the formula: \( x + x+28^{\circ}=180^{\circ} \).

Step3: Simplify the equation

Combine like terms: \( 2x+28^{\circ}=180^{\circ} \). Subtract \( 28^{\circ} \) from both sides: \( 2x=180^{\circ}-28^{\circ}=152^{\circ} \).

Step4: Solve for \( x \)

Divide both sides by 2: \( x=\frac{152^{\circ}}{2}=76^{\circ} \).

Answer:

\( 76 \)