In the adjoining figure abc is an equilateral triangle .if came =75 and bdc=45 prove that bd=ae. (Hint ∆aeb=bcd ,then bd= ae)
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Answer:
Given: AD=BD=AC ∠CAE=75
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In △ABD
AD=BD
∠ABD=∠BAD=x (Isosceles triangle property)
∠ADC=∠ABD+∠BAD=2x (Exterior angle property)
In △ACD
AD=AC
hence, ∠ADC=∠ACD=2x (Isosceles triangle property)
Now, ∠CAE+∠BAC=180 (Linear pair)
75+∠BAC=180
∠BAC=105
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Sum of angles of triangle ABC = 180
∠BAC+∠ABC+∠ACB=180
105+x+2x=180
3x=75
x=25
Thus, ∠ACB=∠ACD=2x=2×25=50
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