Question

in fig 6.28 , find the value of x and y and then show that AB//CD​

Answer 1

Answer:

∠EOA + \angle{x}∠x = 180° [ \therefore∴ liner pair ]

→ 50° + x = 180°

→ x = 180° - 50°

→ x = 130°

Now,

\angle{x}∠x = 130°

\therefore∴ \angle{x}∠x = \angle{CQF}∠CQF = 130°

And

\angle{CQF}∠CQF = \angle{y}∠y [ \therefore∴ Vertically opposite angles ]

Hence,

x = y = 180°

so, they are alternate interior angles

[ \therefore∴ AB ll CD (verified) ]

Answer 2

Answer:

Here, ∠x+50

0 =1800--- straight line

∠x=1800−500∠x=130 0

And ∠y=130 0

--- vertically opposite angles

Thus, ∠x=∠y=130 0

Using Theorem: If two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel.

Thus, AB∥CD

hope it helps