In a quadrilateral ABCD, ∠B = 90° and AD 2 = AB 2 + BC 2 + CD 2, then ∠ACD is equal to:

Q: In a quadrilateral ABCD, ∠B = 90° and AD 2 = AB 2 + BC 2 + CD 2, then ∠ACD is equal to:

In a quadrilateral ABCD, Given :- ∠B = 90° AB2 + BC2 + CD2 = AC2 + CD2 = AD2 { ∴ In triangle ABC , AB2 + BC2 = AC2 } So, in triangle ACD, angle opposite to AD = 90° ( by Converse of Pythagoras theorem) ⇒ ∠ACD = 90°

90°
60°
30°
20°

Correct Answer: 90°

Explanation:

In a quadrilateral ABCD,
Given :- ∠B = 90°
AB² + BC² + CD² = AC² + CD² = AD² { ∴ In triangle ABC , AB² + BC² = AC² }
So, in triangle ACD, angle opposite to AD = 90° ( by Converse of Pythagoras theorem)
⇒ ∠ACD = 90°

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