Question

ABCDE is a five-sided figure in which, BC, CD are respectively equal to AE, DE and
angle(BCD) =angle (DEA). Prove that BE = AC​

Answer 1

Answer:

In △ABC,

⇒  ∠ABC+∠BCA+∠CAB=180o       [ Sum of angles of triangle is 180o. ]  ---( 1 )

In △CDA,

⇒  ∠CDA+∠DAC+∠ACD=180o     [ Sum of angles of triangle is 180o. ]    ---- ( 2 )

In △DEA,

⇒  ∠DEA+∠EAD+∠ADE=180o    [ Sum of angles of triangle is 180o. ]      --- ( 3 )

⇒  Pentagon ABCDE=△ABC+△CDA+△DEA

From ( 1 ), ( 2 ) and ( 3 )

⇒  Pentagon ABCDE=∠ABC+∠BCA+∠CAB+∠CDA+∠DAC+∠ACD+∠DEA+∠EAD+∠ADE

                                         =180o+180o+180o

                                         =540o           ---- ( 4 )

⇒  ∠EAB+∠ABC+∠BCD+∠CDE+∠DEA=Pentagon(ABCDE)

From ( 4 ),

∴  ∠EAB+∠ABC+∠BCD+∠CDE+∠DEA=540o.