Question

in the triangle shown, ( xy cong zy ) and ( mangle y = 38^{circ} ). what is ( mangle z )?

Explanation:

Step1: Use the property of isosceles triangle

Since \(XY\cong ZY\) in \(\triangle XYZ\), \(\angle X=\angle Z\).

Step2: Use the angle - sum property of a triangle

The sum of interior angles of a triangle is \(180^{\circ}\). Let \(\angle X = \angle Z=x\). We know \(\angle Y = 38^{\circ}\). Then \(x + x+38^{\circ}=180^{\circ}\).

Step3: Solve the equation

Combine like terms: \(2x=180^{\circ}- 38^{\circ}=142^{\circ}\). Divide both sides by 2: \(x=\frac{142^{\circ}}{2}=71^{\circ}\).

Answer:

\(71^{\circ}\)