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: