In a ∆ABC, the internal bisectors of the angle B and the angle C intersect at an angle of 105°. What is the value of the angle A?

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SSC CGL 2022 Tier-I Official Paper (Held On : 05 Dec 2022 Shift 3)
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  1. 52.5°
  2. 75°
  3. 15°
  4. 30°

Answer (Detailed Solution Below)

Option 4 : 30°
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Detailed Solution

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Given:

The internal bisectors of angle B and angle C intersect at an angle of 105°

Formula Used:

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In an △ABC, if internal bisectors of angles B and C are joined at D, then

⇒ ∠BDC = 90° + ∠BAC/2

Calculation:

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∠BOC = 105°

Internal bisectors of angles B and C are joined at O

∠BDC = 90° + ∠BAC/2

⇒ 105° = 90° + ∠BAC/2

⇒ 105° - 90° = ∠BAC/2

⇒ 15° = ∠BAC/2

 ∠BAC = 30°

∴ The value of angle A is 30°.

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