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An angle equals five seventh of its supplement. Find the angle and its supplement?
- A35° and 155° respectively
- B45° and 130° respectively
- C60° and 120° respectively
- D75° and 105° respectively
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CCommunity
Let the angle be ‘A’
⇒ Supplement of the angle = (180°– A)
Given that the angle is five seventh of its supplement
⇒ A = 5/7 (180°– A)
⇒ 7 × A = 5 × (180°– A)
⇒ 7A = (5 × 180°)– 5A
⇒ 7A + 5A = (5 × 180°)
⇒ 12A = (5 × 180°)
⇒ A = (5 × 180°)/12
⇒ A = 75°
Supplement of A = 180°– 75° = 105°
∴ Angle and its supplement are 75° and 105° respectively
⇒ Supplement of the angle = (180°– A)
Given that the angle is five seventh of its supplement
⇒ A = 5/7 (180°– A)
⇒ 7 × A = 5 × (180°– A)
⇒ 7A = (5 × 180°)– 5A
⇒ 7A + 5A = (5 × 180°)
⇒ 12A = (5 × 180°)
⇒ A = (5 × 180°)/12
⇒ A = 75°
Supplement of A = 180°– 75° = 105°
∴ Angle and its supplement are 75° and 105° respectively