Question

answer attempt 1 out of 2

m∠xwy=□°

Explanation:

Step1: Identify the triangle type

Since \(XY = XW\), \(\triangle XYW\) is an isosceles triangle. In an isosceles triangle, the base - angles are equal. Let \(\angle XWY=\angle XYW = x\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). So, \(\angle Y+\angle XWY+\angle XYW = 180^{\circ}\). Given \(\angle Y = 42^{\circ}\), and \(\angle XWY=\angle XYW\). Then \(42^{\circ}+x + x=180^{\circ}\).

Step3: Solve the equation for \(x\)

Combine like terms: \(42^{\circ}+2x = 180^{\circ}\). Subtract \(42^{\circ}\) from both sides: \(2x=180^{\circ}- 42^{\circ}=138^{\circ}\). Divide both sides by \(2\): \(x=\frac{138^{\circ}}{2}=69^{\circ}\).

Answer:

\(69\)