In \(\triangle XYZ\), \(XY = XZ\) and \(\angle X = 40°\), what is the measure of \(\angle Z\)?
\(70°\)
Since \(XY = XZ\), triangle XYZ is isosceles, so the base angles opposite the equal sides are equal: \(\angle Y = \angle Z\).
The angles of a triangle sum to \(180°\), so \(\angle Y + \angle Z = 180° - \angle X = 180° - 40° = 140°\).
As \(\angle Y = \angle Z\), each equals \(\frac{140°}{2} = 70°\).
Hence, the measure of \(\angle Z\) is \(70°\).
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