Question

In the below fig, l, m and n are parallel lines intersected by transversal p at X, Y and Z
respectively. Find ∠1, ∠2 and ∠3.

Answer 1

From the given figure:

${\displaystyle \angle }$3 + ${\displaystyle \angle }$m YZ = 180°          [Linear pair]

⇒ ${\displaystyle \angle }$3 = 180° -120°

⇒${\displaystyle \angle }$3 = 60°

Now line l parallel to m

${\displaystyle \angle }$1 = ${\displaystyle \angle }$3              [Corresponding angles]

⇒ ${\displaystyle \angle }$1 = 60°

Also m || n

⇒ ${\displaystyle \angle }$2 =120°                   [Alternative interior angle]

∴ ${\displaystyle \angle }$1 = ${\displaystyle \angle }$3 = 60°

${\displaystyle \angle }$2 = 120°