In the given figure, AB = AD. ∠ACB = 95° + ∠BAC and ∠BAD = 150°. Find ∠ACB.
Answer & explanation
Correct answer: option 4
In the given figure, AB = AD. ∠ACB = 95° + ∠BAC and ∠BAD = 150°.
∠ACB = 95° + ∠BAC
Also in triangle ABC, ∠ACB + ∠BAC + ∠ABC = 180
95° + 2∠BAC + ∠ABC = 180
2∠BAC + ∠ABC = 180° - 95° = 85°
Also, in triangle ABD, ∠ABD + ∠BAD + ∠ADB = 180°
AD = AB, thus ∠ABD = ∠ADB and ∠BAD = 150°
2∠ABD + 150° = 180°
∠ABD = ∠ABC = 15°
2∠BAC + 15° = 85°
∠BAC = 35°
∠ACB + 35 + 15 = 180
∠ACB = 130
The correct answer is Option (4) → 130°