Question

In △ABC, m∠A=50∘, m∠B=60∘, and m∠C=70∘.
If △ABC is rotated 90∘ counterclockwise to △XYZ, what is the measure of angle Z?

Answer 1

Given:

In $\Delta ABC, m\angle A=50^\circ, m\angle B=60^\circ$ and $m\angle C=70^\circ$.

$\Delta ABC$ is rotated $90^\circ$ counterclockwise to $\Delta XYZ$.

To find:

The measure of angle Z.

Solution:

We know that the rotation is a rigid transformation. It means the image and figure are congruent to each other.

$\Delta ABC$ is rotated $90^\circ$ counterclockwise to $\Delta XYZ$. So, $\Delta ABC\cong \Delta XYZ$.

$\angle C\cong \angle Z$                      (CPCTC)

$m\angle C=m\angle Z$

$70^\circ=m\angle Z$

Therefore, the measure of angle Z is 70 degrees.