Question

∆ABC rotates 90° clockwise about point P to form ∆A′B′C′. What is the measure of ∠CPC'?

Answer 1

The measure of ∠CPC' is equal to the measure of the angle ACB.

Step-by-step explanation:

When ∆ABC rotates 90° clockwise about point P to form ∆A′B′C′, the angle CPC' is equal to the angle ACB. This is because rotating a triangle does not change the measures of its angles. Since ∆ABC and ∆A′B′C′ are congruent, it follows that ∠ACB = ∠A′C′B′. Therefore, ∠CPC' = ∠ACB = ∠A′C′B′.

Answer 2

The measure of ∠CPC' after a 90° clockwise rotation of ∆ABC around point P to form ∆A'B'C' is 90°.

Step-by-step explanation:

When ∆ABC is rotated 90° clockwise about a point P to form ∆A'B'C', we are performing a geometric transformation of rotation. Because it's a 90° rotation, all points of ∆ABC will move to a position where they are perpendicular to their initial location in regards to point P.

Point C will move to position C', creating an angle ∠CPC'. Since the rotation is 90° clockwise and if point P is considered at the center of rotation, the measure of ∠CPC' will also be 90°. This is due to the fact that the distance from the point of rotation remains constant during a rotation, and the rotation changes the angle by exactly 90°.

In other words, ∠CPC' is the angle created at point P due to the rotation of point C to C'. As point C has been rotated 90° to reach C', the angle at P, which is ∠CPC', will measure 90°.