If in a triangle ABC as drawn in the figure, AB = AC and ∠ACD = 130°, then ∠BAC is equal to:

F1 SSC Arbaz 18-05-2023 Himanshu D1

This question was previously asked in
SSC CGL 2022 Tier-I Official Paper (Held On : 07 Dec 2022 Shift 4)
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  1. 60°
  2. 50°
  3. 70°
  4. 80°

Answer (Detailed Solution Below)

Option 4 : 80°
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Detailed Solution

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Given:

AB = AC

∠ACD = 130°

Concept Used:

Linear Pair Theorem

Angle sum Property = Sum of all the angles of the triangle is 180°.

Calculation:

In triangle ABC,

∠ACD + ∠ACB = 180°      (Linear Pair)

∠ACB = 180 - 130 = 50° 

Since, AB = AC, 

Triangle ABC is an isosceles triangle.

∠ACB = ∠ABC = 50° 

Apply Angle Sum Property,

∠ACB + ∠ABC + ∠BAC = 180° 

∠BAC = 180 - (50 + 50)

∠BAC = 80° 

Option 4 is the correct answer.

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