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SSC CHSL 2024 PYQ — Question 63

SSC CHSL - 10 July 2024 - Shift 2 • Quantitative Aptitude • Q63

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In an isosceles triangle ABC, AB = AC. D is a point inside the triangle such that ∠BAD = 20° = ∠DCB, ∠CAD = 80°. The value of ∠ABC is:

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. 40∘40^\circ.

Since AB = AC thus, triangle ABC is isosceles

then, ∠BAC = ∠ABC

⇒ ∠BAC = ∠BAD + ∠CAD

⇒ ∠BAC = 20° + 80°

⇒ ∠BAC = 100°

Now, In triangle ABC

⇒ ∠ABC + ∠BCA + ∠BAC = 180°

⇒ ∠ABC + ∠BCA + 100° = 180°

⇒ ∠ABC + ∠BCA = 80°   [∠ABC = ∠BCA]

So,

⇒ ∠ABC + ∠ABC = 80°

⇒ 2∠ABC = 80°

⇒ ∠ABC = 40°