In the figure shown, lines l and m are parallel and lines r and t are transversals. Find x.

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Solution

$∠ A O C + 105^{\circ} = 180^{\circ}$ [Co-interior angles]

Hence, $∠ A O C = 180^{\circ} - 105^{\circ} = 75^{\circ}$ (1 marks)

$∠ A O B = 120^{\circ}$ [Corresponding angles]

$∠ A O B = ∠ A O C + ∠ B O C$ (1 marks)

$\Rightarrow 120^{\circ} = 75^{\circ} + x$

$\Rightarrow x = 120^{\circ} - 75^{\circ} = 45^{\circ}$ (1 marks)

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In the figure shown, lines l and m are parallel and lines r and t are transversals. Find x.

∠AOC+105∘=180∘ [Co-interior angles] Hence, ∠AOC=180∘−105∘=75∘ (1 marks) ∠AOB=120∘ [Corresponding angles] ∠AOB=∠AOC+∠BOC (1 marks) ⇒120∘=75∘+x ⇒x=120∘−75∘=45∘ (1 marks)