Question

triangle ( abc ) is translated 6 units to the right and 4 units up to create triangle ( abc ).
what is the measure of ( angle b )?

Explanation:

Step1: Recall the property of translation

Translation is a rigid transformation. Rigid transformations (such as translation) preserve the shape and size of the figure. So, \(\triangle ABC\cong\triangle A'B'C'\).

Step2: Use the angle - sum property of a triangle

In a triangle, the sum of interior angles is \(180^{\circ}\). For \(\triangle ABC\), if \(\angle A = 80^{\circ}\) and \(\angle C=\angle C' = 20^{\circ}\), then \(\angle B=180^{\circ}-\angle A-\angle C\).
Substitute the values: \(\angle B = 180^{\circ}-80^{\circ}-20^{\circ}\)

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Since \(\triangle ABC\cong\triangle A'B'C'\), \(\angle B=\angle B'\)

Answer:

\(80^{\circ}\)