Question

Q.2) 1. In the fig. measure of same angles are shown using the measures find measures of
y. Show that line i || line m.
130
<xf<y. Show
0
л l
RC
500
2
If+b.
TH​

Answer 1

Answer:

Suppose n is a transversal of the given lines l and m.

Let us mark the points A and B on line l, C and D on line m and P and Q on line n.

Suppose the line n intersects line l and line m at K and L respectively.

Since PQ is a straight line and ray KA stands on it, then

∠AKL+∠AKP=180

∘

(angles in a linear pair)

⇒∠x+130

∘

=180

∘

⇒∠x=180

∘

−130

∘

=50

∘

Since CD is a straight line and ray LK stands on it, then

∠KLC+∠KLD=180

∘

(angles in a linear pair)

⇒∠y+50

∘

=180

∘

⇒∠y=180

∘

−50

∘

=130

∘

Now, ∠x+∠y=50

∘

+130

∘

=180

∘

But ∠x and ∠y are interior angles formed by a transversal n of line l and line m.

It is known that, if the sum of the interior angles formed by a transversal of two distinct lines is 180

∘

, then the lines are parallel.

∴ line l ∥ line m.