# Yeni soruuu

## Elul said

Question:
ABC ikizkenar üçgeni ok yönünde C köşesi etrafında B, C, A’ doğrusal olacak şekilde döndürüyor.
|AB| = |AC|, $\angle$ACB’ = 40°. Buna göre, AA’B’ açısının ölçüsü kaç derecedir?

### Analysis:

Let’s denote:

• \angle BAC = \alpha
• \angle ABC = \angle ACB = \beta (since it is an isosceles triangle ABC with |AB| = |AC|)

From the properties of the isosceles triangle:

\alpha + 2\beta = 180°

### Rotation:

• When triangle ABC is rotated about point C, point A will move to the new position A’.
• The given angle \angle ACB' = 40° represents the angle between lines AC and CB’ after rotation.
• Therefore, \angle ACA' = 40° (since CB and CA are collinear in the new position).

### Finding the angles:

From the rotation:

• Since \angle ACA' = 40°, this is the same as the angle by which the triangle is rotated.

### Calculating \angle AA'B'

As point B didn’t change its position, \angle AA'B' will equal the rotational angle itself:

\angle AA'B' = 40°

Therefore, the measure of angle AA’B’ cannot be derived from rotating just 40°. Observe the options provided:
A) 5
B) 10
C) 15
D) 20
E) 25

It seems none aligns rationally with direct 40° as seen clearer steps to re-confirm logic mathematically considering geometry comprised in options:

Finally,