In a triangle ABC AB AC ang BAC 40 deg Then the external angle at B is ........

Quantitative Aptitude ( CCS) Geometry

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In a triangle ABC, AB = AC, ∠BAC = 40°. Then the external angle at B is :

90°

70°

110°

80°

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Explanation:

AB = AC
∴ ∠ACB = ∠ABC
∠BAC = 40° (given)
In ΔABC, we know that
∠ABC + ∠ACB + ∠BAC = 180°
∠ABC + ∠ABC + 40° = 180° [? ∠ABC = ∠ACB]
2∠ABC = 180° – 40° = 140°
∠ABC = 70°
External angle, ∠ABD = 180° – 70° = 110°