Question

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

Explanation:

Step1: Use the property of isosceles triangle

Since two sides of the triangle are equal (marked with the same tick), the triangle is isosceles. In an isosceles triangle, the angles opposite the equal sides are equal. But here, we know that the sum of angles in a triangle is \(180^{\circ}\). Let \(w\) and the un - named angle (opposite to the equal side) be equal. Let the third angle \(H = 75^{\circ}\).

Step2: Calculate \(w\)

We know that \(w + x+75^{\circ}=180^{\circ}\). Also, because the triangle is isosceles (two equal sides), \(w=x\). Substitute \(x = w\) into the angle - sum formula: \(w + w+75^{\circ}=180^{\circ}\). Combine like terms: \(2w=180^{\circ}-75^{\circ}\). So \(2w = 105^{\circ}\), then \(w=\frac{105^{\circ}}{2}=37.5^{\circ}\). Since \(x = w\), \(x = 37.5^{\circ}\)

Answer:

\(w = 37.5\), \(x = 37.5\)