(a) Prove that when two lines intersect, the vertically opposite angles are equa

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(a) Prove that when two lines intersect, the vertically opposite angles are equal.
(b) Find the value of x from the given figure: [3 MARKS]

Options:

Answer: Option A
:

(a) Proof: 2 Marks
(b) Solution: 1 Mark
(a)

We have to prove $∠ 1 = ∠ 3 & ∠ 2 = ∠ 4$
$∠ 1 + ∠ 2 = 180^{\circ}$ [Linear pair]
$\Rightarrow ∠ 1 = 180^{\circ} - ∠ 2$
Again, $∠ 3 + ∠ 2 = 180^{\circ}$ [Linear pair]
$\Rightarrow ∠ 3 = 180^{\circ} - ∠ 2$
Hence, $∠ 1 = ∠ 3$
Similarly, we can prove that $∠ 2 = ∠ 4$ .
(b) $∠$ AOB = $∠$ DOE (vertically opposite angles)
$∴ ∠$ x = 60 $^{\circ}$

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