Pimilar Palygons T. Thangle DEF is a dilation of triangle ABC with scale factor 2 . In triangle ABC, the largest angle measures \( 82^{\circ} \). What is the largest angle measure in triangle DEF? \( \begin{array}{ll}\text { (A) } 41 & \text { (C) } 123^{\circ} \\ \begin{array}{ll}\text { B. } 82^{\circ} & \text { (D) } 164^{\circ}\end{array}\end{array} \)

In dilation, the shape is resized but retains its angles, so the measures of the angles remain unchanged regardless of the scale factor. Therefore, since triangle DEF is a dilation of triangle ABC, the largest angle in triangle DEF will also measure \( 82^{\circ} \). Imagining real-world situations, this type of geometric transformation appears in architecture and design. When engineers or architects create scaled models of buildings, they use dilation to ensure that the proportions and angles of the structures remain consistent, allowing for accurate representations in a smaller or larger form without altering the original design's angle measures.