Question

ABC is a triangle in which DE || BC , find <A​

Answer 1

Answer:

/_A = 35°

Step-by-step explanation:

In ∆BCE,

80° + 30° + /_C = 180°

/_C = 180° - 110° = 70°

Since, DE || BC & BE is transversal,

Therefore, /_EBC = /_DEB = 30°

hence, /_DEC = 80° + 30° = 110°

Now, in quadrilateral DBCE,

/_D + /_B + /_E + /_C = 360° (Angle Sum Property)

105° + /_B + 110° + 70° = 360°

/_B = 360° - 285° = 75°

Now, in ∆ABC

/_A + /_B + /_C = 180° (Angle Sum Property)

/_A + 75° + 70° = 180°

/_A = 180° - 145° = 35°

Hope it helps!!

Have a great day!!