Question

what is the value of w?

w = 1^{circ}

Explanation:

Step1: Recall the property of isosceles triangle

In triangle \(FGH\), since \(FG = GH\) (marked with the same tick - mark), triangle \(FGH\) is an isosceles triangle. In an isosceles triangle, the base - angles are equal. Let \(\angle F=\angle H = w\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). For \(\triangle FGH\), we have \(\angle F+\angle G+\angle H = 180^{\circ}\). Substitute \(\angle F = w\), \(\angle H = w\), and \(\angle G=64^{\circ}\) into the equation: \(w + 64^{\circ}+w=180^{\circ}\).

Step3: Solve the equation for \(w\)

Combine like terms: \(2w+64^{\circ}=180^{\circ}\). Subtract \(64^{\circ}\) from both sides: \(2w=180^{\circ}-64^{\circ}\). So \(2w = 116^{\circ}\). Divide both sides by 2: \(w=\frac{116^{\circ}}{2}\).

Answer:

\(58\)