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

Answer:70

Explanation:

Answer 2

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.