Question

in the given figure, BA parallel to ED and BC parallel to EF. show that angle ABC + angle DEF = 180 degree​

Answer 1

Answer:

Pls refer to the attached diagram and explanation

Step-by-step explanation:

First we expand EF such that it intersects at AB and expand ED such  that it intersects BC

Now;

∵AB║ED

∴∠ABC=∠EXC       [Corresponding Angles]

And

∵BC║EF

∵∠EXC=∠AED=∠ABC    [Alternate Angles]

Now;

∠AED + ∠ DEF = 180°   [Supplementary Angles]

∴ ∠ABC + ∠DEF = 180° [Because ∠ABC = ∠EXC = ∠AED

[You can name the point of intersection of AB and EF as anything ,here i have considered it as A]