Method I: In the given figure, let us assume that
AOB is a straight line
∴ ∠x + ∠y = 180°
(linear pair of angles) …(i)
and ∠p + ∠q = 180°
(linear pair of angles) …(ii)
From (i) and (ii), we get
∠x + ∠y = ∠p + ∠q
Hence proved
Method II: As we know that sum of the angles around a point is 360°.
∴ ∠x + ∠y + ∠p + ∠q = 360°
or ∠x + ∠y + ∠x + ∠y = 360°
(∵ ∠x + ∠y = ∠p + ∠q)
2 (∠x + ∠y) = 360°
⇒ ∠x + ∠y = 180°
⇒ AOB is a straight line.
