Question

question
find ( mangle wyx ).

Explanation:

Step1: Recall the property of isosceles triangle

In \(\triangle WXY\), \(WX = XY\) (marked with the same tick - marks), so \(\triangle WXY\) is an isosceles triangle. The sum of interior angles of a triangle is \(180^{\circ}\). Let \(m\angle W = m\angle Y\) (base angles of an isosceles triangle are equal).

Step2: Set up the equation

Let \(m\angle W = m\angle Y=x\). We know that \(m\angle X = 127^{\circ}\). Using the angle - sum property of a triangle \(m\angle W+m\angle Y+m\angle X=180^{\circ}\). Substitute the values: \(x + x+127^{\circ}=180^{\circ}\).

Step3: Solve the equation

Combine like terms: \(2x=180^{\circ}- 127^{\circ}\). So \(2x = 53^{\circ}\), then \(x=\frac{53^{\circ}}{2}=26.5^{\circ}\).

Answer:

\(m\angle WYX = 26.5^{\circ}\)