Question

please solve this question ​

Answer 1

Answer:

Given : l & m are two lines intersected by a transversal line p

∠ 1 = 130°

∠ 8 = 50 °

To prove : l || m

Proof :

It is given that line l is intersected by p,

∴ ∠ 1 = ∠ 3 ( Vertically Opposite Angle)

∠ 3 = 130 ° ----(1)

And, ∠ 3 & ∠ 4 forms linear pair.

Similarly, line m is intersected by p,

∴ ∠ 8 = ∠ 6 ( Vertically Opposite Angle)

∠6 = 50 ° ----(2)

And, ∠ 6 & ∠ 5 forms linear pair.

Now, ∠ 3 + ∠ 4 = 180° ( ∠ 3 = 130° )

∠ 4 = 180° - 130 °

∠ 4 = 50° ----(3)

And, ∠ 6 + ∠ 5 = 180° ( ∠ 6 = 50° )

∠ 5 = 180°- 50°

∠ 5 = 130° ----(4)

From (1), (2), (3) &(4) we get,

∠ 3 = ∠ 5 and ∠ 4 = ∠ 6 are pairs of alternate interior angles as line l & m is intersected by line p.

We know that, if the alternate interior angles, the angles that are on opposite sides of the transversal and inside the parallel lines, are equal, then the lines are parallel.

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