In triangle ABC, D and E are the points on AB and AC respectively such that AD x AC = AB x AE. If ∠ADE = ∠ACB + 30° and ∠ABC = 78°, then ∠A= ?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 54°.
AD × AC = AB × AE
AD/AB = AE/AC
Hence triangle ABC is similar to triangle ADE.
So,
∠ADE = ∠ABC And ∠AED = ∠ACB
∠ADE = 78° and ∠ADE = ∠ACB + 30° [Given]
⇒ ∠ACB = 78° - 30° = 48°
In triangle ABC:
∠ABC + ∠ACB + ∠A = 180°
⇒ ∠A = 180° - ∠ABC + ∠ACB
⇒ ∠A = 180° - (78° - 48°)
⇒ ∠A = 54°