in the given five sided closed figure find angle eab + angle bcd + angle cde angle dear
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Step-by-step explanation:
In △ABC,
⇒ ∠ABC+∠BCA+∠CAB=180
o
[ Sum of angles of triangle is 180
o
. ] ---( 1 )
In △CDA,
⇒ ∠CDA+∠DAC+∠ACD=180
o
[ Sum of angles of triangle is 180
o
. ] ---- ( 2 )
In △DEA,
⇒ ∠DEA+∠EAD+∠ADE=180
o
[ Sum of angles of triangle is 180
o
. ] --- ( 3 )
⇒ Pentagon ABCDE=△ABC+△CDA+△DEA
From ( 1 ), ( 2 ) and ( 3 )
⇒ Pentagon ABCDE=∠ABC+∠BCA+∠CAB+∠CDA+∠DAC+∠ACD+∠DEA+∠EAD+∠ADE
=180
o
+180
o
+180
o
=540
o
---- ( 4 )
⇒ ∠EAB+∠ABC+∠BCD+∠CDE+∠DEA=Pentagon(ABCDE)
From ( 4 ),
∴ ∠EAB+∠ABC+∠BCD+∠CDE+∠DEA=540
o
.
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