Q6 of 32 Page 60

In figure 5.34 BA || ED and BC || EF. Show that ∠ABC + ∠DEF = 180°.

Given.


BA || ED and BC || EF


Construction.


Extend ray ED and let it intersect at line BC


Theory.


⇒ If 2 lines are parallel then their corresponding angles are equal


⇒ If 2 lines are parallel then sum of their internal angles is 180°


Solution


As AB || DE


And CB is transverse


Then by corresponding angles


⇒ ∠ ABC = ∠ CDE


As CB || EF


And DE is transverse


Then by interior angles


⇒ ∠ FED + ∠ CDE = 180°


Hence ;


⇒ ∠ FED + ∠ ABC = 180°


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