Question

In figure 2.24, measures of some angles
are shown. Using the measures find the
measures of angle x and angle y and hence show that line l || line m.​

Answer 1

angle x = 130°...........(vertically opposite angle)

angle y =50°.............(vertically opposite angle)

Let us consider angle z as I had showed in figure

angle z + 50° = 180° (must be 180°, so we can prove that line l is parallel to line m) (alternate interior angles)

angle z = 180° - 50°

angle z = 130°

(we got angle z by adding angle z to 50° ,we are getting 180°)

alternate interior angles are supplementary means line l and line m are parallel

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Answer 2

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.