Question

in the given figure find the value of x and y and then show that AB is parallel to CD

Answer 1

By vertically opposite angle Y=130° and by alternate interior angle Y=X= 130°

Answer 2

y=130° [ Since y is vertically opposite to 130°]

x=180°-50° [ Since x and 50° are linear pairs]
→x=130°

It is Clear now x and y are the same [130°].

But x and y are Alternate interior angles...

If alternate interior angles so Formed by a Transversal are the same.. Then The Transversal Cut's Parallel Lines...

→The Lines Are parallel... As a transversal Passes through Parallel Lines and form equal Alternate interior angles...

Hope it Helps....

I doubt if It is Alternate Interior angles or if it is called as Alternate Interior opposite angles...

Regards,
Leukonov.