Question

in the figure ABCDE , find angle 1 + angle 2 + angle 3 + angle 4 + angle 5 . A = 1 B =2 C =3 D = 4 E =5​

Answer 1

Answer:

In △ABE,

∠A+∠ABE+∠AEB=180o         ---- ( 1 )

In △BDE,

∠DBE+∠BDE+∠BED=180o             ------ ( 2 )

In △BCD,

∠CBD+∠C+∠CDB=180o           ----- ( 3 )

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

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

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

⇒  ∠A+∠B+∠C+∠D+∠E=540o

∴  ∠1+∠2+∠3+∠4+∠5=540o