Question

In the following figure, ∠BAC = 90°, AD ⊥ BC and ∠BAD = 50°, then ∠ACD is ______.

Options

• 50°

• 40°

• 70°

• 60°

Answer 1

In the following 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°