Question

what are the values of w and x?

Explanation:

Step1: Identify the triangle type

Since two sides of \(\triangle EFG\) are equal (marked with the same tick), \(\triangle EFG\) is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. So \(x = w\).

Step2: Use the triangle - angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So \(x + w+61^{\circ}=180^{\circ}\). Substitute \(x = w\) into the equation: \(2w+61^{\circ}=180^{\circ}\).

Step3: Solve for \(w\)

Subtract \(61^{\circ}\) from both sides of the equation \(2w+61^{\circ}=180^{\circ}\): \(2w=180^{\circ}-61^{\circ}=119^{\circ}\). Then divide both sides by 2: \(w=\frac{119^{\circ}}{2} = 59.5^{\circ}\). Since \(x = w\), \(x = 59.5^{\circ}\).

Answer:

\(w = 59.5\), \(x = 59.5\)