Question

what are the values of $w$ and $x$?

Explanation:

Step1: Identify the triangle type

Since two sides are equal (marked with red ticks), it is an isosceles triangle. In an isosceles triangle, the base - angles are equal. So \(x = 35^{\circ}\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let \(w\) be the vertex angle. Then \(w+x + 35^{\circ}=180^{\circ}\). Substitute \(x = 35^{\circ}\) into the equation: \(w+35^{\circ}+35^{\circ}=180^{\circ}\). Simplify the left - hand side: \(w + 70^{\circ}=180^{\circ}\). Solve for \(w\) by subtracting \(70^{\circ}\) from both sides: \(w=180^{\circ}-70^{\circ}\).

Answer:

\(w = 110^{\circ}\), \(x = 35^{\circ}\)