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In the adjoining figure, ∠ABC = 90°, ∠BCA = 50° and BD ⊥ AC. Then ∠ABD =

In the adjoining figure, ∠ABC = 90°, ∠BCA = 50° and BD ⊥ AC. Then ∠ABD = R.S. Aggarwal Mathematics Solutions ICSE Class 9.

  1. 30°

  2. 40°

  3. 50°

  4. 60°

Triangles

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Answer

In △ABC,

By angle sum property of triangle,

⇒ ∠A + ∠B + ∠C = 180°

⇒ ∠A + 90° + 50° = 180°

⇒ ∠A + 140° = 180°

⇒ ∠A = 180° - 140°

⇒ ∠A = 40°.

In △ABD,

By angle sum property of triangle,

⇒ ∠A + ∠ABD + ∠D = 180°

⇒ 40° + ∠ABD + 90° = 180°

⇒ ∠ABD + 130° = 180°

⇒ ∠ABD = 180° - 130°

⇒ ∠ABD = 50°.

Hence, option 3 is the correct option.

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