Mathematics
In the adjoining figure, 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
50°
30°
60°
100°
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Answer
Considering △APB and △CPD,
and ∠APB = ∠CPD (Vertically opposite angles are equal)
∴ △APB ~ △CPD
Hence, ∠PAB = ∠PDC = 30°
∠PBA = 180° - (∠PAB + ∠APB) = 180° - (30° + 50°) = 180° - 80° = 100°.
Hence, Option 4 is the correct option.
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