In Fig.6.3, two line segments AC and BD intersect each other at the point P such that PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, ∠ APB = 50° and ∠ CDP = 30°. Then, ∠ PBA is equal to

(A) 50° (B) 30° (C) 60° (D) 100°

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Question 7
In Fig.6.3, two line segments AC and BD intersect each other at the point P such that PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, ∠ APB = 50° and ∠ CDP = 30°. Then, ∠ PBA is equal to
(A) 50° (B) 30° (C) 60° (D) 100°
In Δ APB and Δ DPC
𝐴𝑃/𝐵𝑃=𝐷𝑃/𝐶𝑃
∠ APB = ∠ DPC
∴ Δ APB ~ Δ DPC
(Both ratios are same)
(Vertically opposite angles)
(SAS Similarity)
Since both triangles are similar
Their angles will be equal
∴ ∠ PAB = ∠ PDC = 30°
Now,
In Δ APB,
∠ ABP + ∠ PAB + ∠ APB = 180°
∠ ABP + 30° + 50° = 180°
∠ ABP + 80° = 180°
∠ ABP = 180° − 80°
∠ ABP = 100°
So, the correct answer is (D)
(Angle sum property)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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