Answer:
∠A = 35°
Explanation:
From the question above,
Sum of Angles on a straight line = 180°
180° = ∠BDE + ∠ADE
∠BDE = 105°
∠ADE = 180° - 105°
∠ADE = 75°
To find Angle ∠EBC and ∠DEB are alternate angles, this means that they are equal to each other
Hence, ∠EBC = ∠DEB
30° = 30°
Sum of Angles on a straight line = 180°
180° = ∠DEB + ∠BEC + ∠DEA
180° = 30° + 80° + ∠DEA
∠DEA = 180° -(30+ 80)°
∠DEA = 180° - 110°
∠DEA = 70°
It is important to note that the sum of Angles in a triangle = 180°
180° = ∠ADE + ∠DEA + ∠A
∠ADE = 75°
∠DEA = 70°
180° = 75° + 70° + ∠A
∠A = 180° - (75° + 70°)
∠A = 180° - 145°
∠A = 35°