In Δ ABD, BD is extended to E, AD = 120°, AC ⊥ BD. Find x and y respectively.

- x = 30°, y = 75°
- x = 15°, y = 75°
- x = 15°, y = 80°
- x = 30°, y = 80°

Option 2 : x = 15°, y = 75°

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Given:

∠ADE = 120°

∠ACD = 90°

Concept:

The sum of all interior angles in a triangle is 180°.

Angles are linear if they are adjacent angles formed by two intersecting lines.

Calculation:

∠ADE + ∠ADC = 180° (Linear pair of angles)

⇒ ∠ADC = 180° - 120°

⇒ ∠ADC = 60°

In ΔADC,

∠CAD + ∠ADC + ∠DCA = 180°

⇒ 2x + 60° + 90° = 180°

⇒ 2x = 30°

⇒ x = 15°

So,

⇒ 3x = 3 × 15° = 45° = ∠DAB

In ΔABD,

∠ADB + ∠ABD + ∠DAB = 180°

⇒ y + 60° + 45° = 180°

⇒ y = 180° - 105°

⇒ y = 75°

∴ x = 15°, y = 75°

The correct option is 2 i.e. x = 15°, y = 75°

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