Question

in the given figure l is parallel to m . Show that ∠1 +∠2 -∠3 is 180°

Answer 1

Given ,

l // m ,

produce BC intersects DE at F .

i ) l // m , BF is the transversal.

<1 + x = 180°

[sum of Interior angles same side of

the transversal are supplementary ]

x = 180° - <1 ----( 1 )

ii ) <2+ y = 180°

y = 180° - <2 ----( 2 )

[ Linear pair ]

iii ) In ∆CDF ,

<3 + x + y = 180° ----( 3 )

[ Angle sum property ]

Substitute ( 1 ) and ( 2 ) in ( 3 ) ,we get

<3 + 180° - <1 + 180° - <2 = 180°

=> 180° = 180° -180° + <1 + <2 - <3

=> 180° = <1 + <2 - <3

Hence , proved.

••••

Answer 2

This is the answer

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