**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:

**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:

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,

**Answer:**

Let’s conclude proper logic - Although geometrical interim debug retained logically nearest recheck yielding possible boxed interpretations defining: