Question

in figure ABCDE find angle 1+2+3+4+5​

Answer 1

Answer:

In △ABE,

∠A+∠ABE+∠AEB=180

o

---- ( 1 )

In △BDE,

∠DBE+∠BDE+∠BED=180

o

------ ( 2 )

In △BCD,

∠CBD+∠C+∠CDB=180

o

----- ( 3 )

Now, adding equation ( 1 ), ( 2 ) and ( 3 )

⇒ ∠A+∠ABE+∠AEB+∠DBE+∠BDE+∠BED+∠CBD+∠C+∠CDB=180

o

+180

o

+180

o

⇒ ∠A+∠ABE+∠DBE+∠CBD+∠C+∠BDE+∠CDB+∠AEB+∠BED=540

o

⇒ ∠A+∠B+∠C+∠D+∠E=540

o

∴ ∠1+∠2+∠3+∠4+∠5=540

o

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