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प्रश्न
In the given figure, ∠BAC = 90°, AD ⊥ BC and ∠BAD = 50°, then ∠ACD is ______.
विकल्प
50°
40°
70°
60°
उत्तर
In the given figure, ∠BAC = 90°, AD ⊥ BC and ∠BAD = 50°, then ∠ACD is 50°.
Explanation:
Given, ∠BAC = 90°, AD ⊥ BC and ∠BAD = 50°
In ΔABD, ∠ABD + ∠DAB + ∠ADB = 180° ......[Angle sum property of a triangle]
⇒ ∠ABD + 50° + 90° = 180°
⇒ ∠ABD + 40° = 180°
⇒ ∠ABD = 180° – 40°
⇒ ∠ABD = 40°
Now, In ΔABC, ∠A + ∠B + ∠C = 180° ......[Angle sum property of a triangle]
⇒ 90° + 40° + ∠C = 180°
⇒ ∠C = 180° – 130°
⇒ ∠C = 50°
∴ ∠ACD = 50°
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