Üçgende Açıortay Özellikleri

Soru

ABC üçgeninde

[AD] ve [BE] açıortay

$m(\widehat{BAD}) = \alpha$

$m(\widehat{CBE}) = \beta$

$m(\widehat{ACB}) = 80^\circ$

Buna göre, $\beta - \alpha$ farkı kaç derecedir?

A) 20

B) 40

C) 50

D) 80

E) 100

Soruda görsel içerik var: A geometric figure shows an ABC triangle with lines [AD] and [BE] intersecting at point D. Both [AD] and [BE] are angle bisectors. The angle $\alpha$ is marked at vertex A for angle BAD. Angle $\beta$ is marked at vertex B for angle CBE. There is another point E outside the triangle. Lines connect A to E, B to E, and C to E. The angle at vertex C inside the ABC triangle is given as $80^\circ$. The diagram explicitly shows that the angle at B is divided into two equal parts marked with dots, and the angle at A is divided into two equal parts marked with small lines.