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In triangle PQR, points A, B and C are taken on PQ, PR and QR respectively such that QC = AC and CR = CB. If ∠QPR = 40°, then ∠ACB is equal to :
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- 140°
- 40°
- 70°
- 100°
- 140°
Correct Option: D
According to question , we draw a figure of a triangle PQR in which points A, B and C are taken on PQ, PR and QR respectively
Given that , ∠QPR = 40°
AC = QC
∴ ∠QAC = ∠CQA = y ( say )
CR = CB
∴ ∠ CBR = ∠CRB = z
∴ From ∆ PQR,
∠y + ∠z + 40° = 180°
∠y + ∠z = 140° ......(i)
Again, ∠ ACQ + ∠ ACB + ∠ BCR = 180°
⇒ 180° – 2y + ∠ ACB + 180° – 2z = 180°
⇒ ∠ ACB = 2 (y + z) – 180° = 2 × 140 – 180° = 100°
