Question
Two adjacent angles forming a linear pair are in the ratio 7:5, find the angles.
✓
Answer
In the given figure, ∠AOC and ∠BOC are adjacent angles which form a linear pair
∴ ∠AOC ∠BOC = 180°
But ∠AOC : ∠BOC = 7 : 5
Let ∠AOC = 7x and ∠BOC = 5x
∴ 7x + 5x = 180°
⇒ 12x = 180°
$\Rightarrow x=\frac{180^{\circ}}{12}=15^{\circ}$
∴ ∠AOC = 7x = 7 × 15 = 105°
and ∠BOC = 5x = 5 × 15 = 75°
∴ ∠AOC ∠BOC = 180°
But ∠AOC : ∠BOC = 7 : 5
Let ∠AOC = 7x and ∠BOC = 5x
∴ 7x + 5x = 180°
⇒ 12x = 180°
$\Rightarrow x=\frac{180^{\circ}}{12}=15^{\circ}$
∴ ∠AOC = 7x = 7 × 15 = 105°
and ∠BOC = 5x = 5 × 15 = 75°
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