Question

please answer this question

Answer 1

Answer:

Step-by-step explanation:

to proof : angle ACE = 1/2 (angle ABE)

now lets proof but before that here is your required diagram in the attachment!

As ABE is an equilateral triangle, hence

∠ABE=60 degree .......(i)

AB=BE

And ABCD is a square hence

∠ABC=90 degree

AB=BC........(ii)

By (i) and (ii) we get

BC=BE

In triangle BCE

∠BEC=∠BCE [angles opposite to equal sides are equal]

Also

⟹∠BEC+∠BCE+∠CBE=180 degree [Angle sum property]

⟹∠BCE+∠BCE+(∠ABC+∠ABE)=180 degree

2⟹∠BCE+(90 degree+60 degree)=180 degree

2⟹∠BCE=180 degree−150 degree

⟹∠BCE=15 degree

As diagonals of the square bisect the interior angle, hence

∠ACD=90 degree=45 degree

∠BCD=∠ACD+∠ACE+∠BCE

⟹90 degree=45 degree+∠ACE+15 degree

⟹∠ACE=90 degree−60 degree

⟹∠ACE=30 degree

⟹∠ACE=12(60 degree)

⟹∠ACE=1/2(∠ABE)

hope it helps!!

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