Açıların Toplamı ve Üçgenler

1. Aynı düzlemde bulunan ve ortak köşesi $K$ olan şekildeki üçgenler için $m(\widehat{AKF}) = 65^\circ$, $m(\widehat{BKC}) = 80^\circ$ ve $m(\widehat{DKE}) = \alpha$'dır.

$a_1 + a_2 + a_3 + a_4 + a_5 + a_6 = 380^\circ$ olduğuna göre,

$m(\widehat{DKE}) = \alpha$ kaç derecedir?

A) 35

B) 40

C) 45

D) 50

E) 55

Soruda görsel içerik var: The image displays three triangles with a common vertex K. The yellow triangle (ABK) has vertices A, B, K with angle a1 at A and a2 at B. The blue triangle (FKE) has vertices F, K, E with angle a6 at F and a5 at E. The pink triangle (CKD) has vertices C, K, D with angle a3 at C and a4 at D. The central region around point K is divided into several angles: the angle between AK and FK is 65 degrees, the angle between BK and CK is 80 degrees, and the angle between DK and EK is alpha. The vertices are arranged around the common vertex K.