ABC is a triangle in which DE ∥BC. Find ∠A

∠A = 35°

Step-by-step 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°

step-by-step explanation: