Question

2a. \\( \triangle abc \\) is reflected over line \\( l \\) to get \\( \triangle a ^ { prime } b ^ { prime } c ^ { prime } \\). if the \\( m \angle c ^ { prime } \\) is \\( 53 ^ { circ } \\), then find \\( m \angle b ^ { prime } \\).

Explanation:

Step1: Use reflection property

Since \(\triangle ABC\) is reflected over line \(l\) to get \(\triangle A'B'C'\), \(\triangle ABC\cong\triangle A'B'C'\) (reflection is a rigid transformation). So, \(\angle B=\angle B'\), \(\angle C = \angle C'\), \(\angle A=\angle A'\)

Step2: Use triangle angle - sum property

In \(\triangle ABC\), \(\angle A+\angle B+\angle C = 180^{\circ}\). From the original triangle (assuming the un - labeled angle in \(\triangle ABC\) is \(\angle A = 90^{\circ}\) as it looks like a right - triangle from the figure), and \(\angle C=\angle C' = 53^{\circ}\)

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Answer:

\(m\angle B'=37^{\circ}\)