Question

question
find ( mangle xwy ).

Explanation:

Step1: Identify the triangle type

Since two sides of the triangle \( \triangle XWY\) are equal (marked with the same tick - marks), \( \triangle XWY\) is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. So \( \angle XWY=\angle YXW\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle XWY = m\angle YXW=x\). We know that \(m\angle Y = 42^{\circ}\). Then, by the angle - sum property of a triangle \(x + x+42^{\circ}=180^{\circ}\).
Simplify the equation: \(2x=180^{\circ}- 42^{\circ}\). So \(2x = 138^{\circ}\).
Solve for \(x\): \(x=\frac{138^{\circ}}{2}=69^{\circ}\).

Answer:

\(69^{\circ}\)