Question

C
E
Fig. 10.120
In Fig. 10.121, arms BA and BC of ZABC are respectively parallel to arms ED and EF
of ZDEF. Prove that ZABC + ZDEF = 180°.
Fig. 10.121​

Answer 1

Answer:

It's given that AB||ED And EF || BC

We'll do a little construction here and extend the lone ED and BC until they intersect at point G

Now,

As EF||BC,

And here BG is is acting as a transversal,

Therefore,

∠ EGB = ∠ DEF (by alternate interior ∠s) -----(i)

Now,

AS AB|| ED

Then,

∠ ABC + ∠ EGB = 180° (interior angles on thr same side of transversal).---(ii)

By substituting for EGB of eq (i) in eqe (ii).

It becomes,

∠ABC+∠DEF= 180°

hope it's help u.......