Question

given △abc is located on the coordinate plane ∠a measures 78° if the triangle is rotated 45° clockwise about the origin to form △abc, what is the measure of ∠a? 39° 45° 78° 102°

Explanation:

Step1: Recall the property of rotation

Rotation is a rigid transformation. Rigid transformations (such as rotation) preserve the measures of angles in a figure.

Step2: Apply the property to the angle

Since \(\triangle ABC\) is rotated to form \(\triangle A'B'C'\), the measure of \(\angle A\) in \(\triangle ABC\) is equal to the measure of \(\angle A'\) in \(\triangle A'B'C'\). Given that \(\angle A = 78^{\circ}\), then \(\angle A'=78^{\circ}\)

Answer:

\(78^{\circ}\)