(a) In the given figure, prove that LX∥MY∥NZ. [3 MARKS](b) If k=50∘, the

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(a) In the given figure, prove that $L X ∥ M Y ∥ N Z$ . [3 MARKS]

(b) If $k = 50^{\circ}$ , then find the value of $∠ P S Y$ .

Options:

Answer: Option A
:

(a) Steps: 1 Mark
Proof: 1 Mark
(b) Solution: 1 Mark
(a) $∠ X P B = ∠ M S P = k$ (Alternate Angles are equal)
$\Rightarrow L X ∥ M Y . . . (i)$ .
$∠ P S M = ∠ S R N = k$ (Corresponding Angles)
$\Rightarrow M Y ∥ N Z . . . . (i i)$ .
From (i) and (ii)
$L X ∥ M Y a n d M Y ∥ N Z$
$\Rightarrow L X ∥ M Y ∥ N Z$ .
(b) Given $k = 50^{\circ}$ ,
$∠ P S Y = 180^{\circ} - k$
$= 180^{\circ} - 50^{\circ} = 130^{\circ}$

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