Questions: Noah draws triangle ABC. Then, he translates that triangle using the rule (x+2, y-1) to create triangle A'B'C'. The measure of angle A is 60 degrees. What is the measure of angle A' in degrees?

Solution Steps

The problem involves a translation of a triangle, which is a type of rigid transformation. Rigid transformations, such as translations, rotations, and reflections, do not change the measures of angles in a shape. Therefore, the measure of angle \( \angle A^{\prime} \) will be the same as the measure of \( \angle A \).

A translation is a type of rigid transformation that shifts a shape in the plane without altering its size or shape. This means that the internal angles of the shape remain unchanged. Therefore, the measure of angle \( \angle A^{\prime} \) in the translated triangle \( A^{\prime}B^{\prime}C^{\prime} \) will be the same as the measure of angle \( \angle A \) in the original triangle \( ABC \).

The translation rule given is \((x+2, y-1)\). This rule shifts each point of the triangle by adding 2 to the \( x \)-coordinate and subtracting 1 from the \( y \)-coordinate. However, this operation does not affect the measure of the angles in the triangle.

Since the translation does not change the measure of the angles, the measure of \( \angle A^{\prime} \) is the same as the measure of \( \angle A \), which is 60 degrees.

Final Answer