(a) In the given figure, prove that lines lm & nq are parallel to each other

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(a) In the given figure, prove that lines lm & nq are parallel to each other.

(b) Find the value of "x” if AB is parallel to CD.

[3 MARKS]

Options:

Answer: Option A
:

(a) Steps: 1 Mark
Proof: 1 Mark
(b) Solution: 1 Mark
(a) Given, $∠ L S T = 105^{\circ}$ and $∠ N T S = 75^{\circ}$
$∠ L S T + ∠ N T S = 105^{\circ} + 75^{\circ} = 180^{\circ}$
These are co-interior angles.
Since co-interior angles are supplementary, lines are parallel.
Hence, the lines LM and NQ are parallel.
(b) Since AB is parallel to CD, corresponding angles will be equal.

Therefore, x = 130°

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