Question

suppose \\( \triangle a b c \cong \triangle x y z, m \angle a=50^{\circ} \\), and\\( m \angle y=70^{\circ} \\).
what is \\( m \angle c \\)?
\\( 50^{\circ} \\)
\\( 60^{\circ} \\)
\\( 70^{\circ} \\)
\\( 110^{\circ} \\)

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle ABC\cong\triangle XYZ\), then \(\angle B=\angle Y\). Given \(m\angle Y = 70^{\circ}\), so \(m\angle B=70^{\circ}\).

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). For \(\triangle ABC\), we know that \(m\angle A + m\angle B+m\angle C=180^{\circ}\). Given \(m\angle A = 50^{\circ}\) and \(m\angle B = 70^{\circ}\).
Substitute the values into the formula: \(50^{\circ}+70^{\circ}+m\angle C=180^{\circ}\).
Then \(m\angle C=180^{\circ}-(50^{\circ} + 70^{\circ})\).
\(m\angle C=180^{\circ}-120^{\circ}\).

Answer:

\(60^{\circ}\) (the second option)