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Mathematics

In the given figure, if ∠ACD = 30° and ∠BPD = 100°, then ∠CDB is equal to :

  1. 30°

  2. 40°

  3. 50°

  4. 60°

In the given figure, if ∠ACD = 30° and ∠BPD = 100°, then ∠CDB is equal to. Loci, RSA Mathematics Solutions ICSE Class 10.

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Answer

∠ABD = ∠ACD = 30° [Angles in the same segment]

From figure,

∠PBD = ∠ABD = 30°

In ΔPBD,

By angle sum property,

∠PBD + ∠BPD + ∠PDB = 180°

30° + 100° + ∠PDB = 180°

∠PDB = 180° - 130°

∠PDB = 50°.

From figure,

∠CDB = ∠PDB = 50°.

Hence, option 3 is the correct option.

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