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Question

ABC is an isosceles triangle and AB = AC. If side BA is produced to D such that BA = AD, what is the measure of DCB?



A

 30

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B

 60

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C

 90

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D

 120

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Solution

The correct option is B

 90


In ABC,AB=AC.
We know, a
ngles opposite to equal sides of a triangle are equal.
So, ABC=ACB=1  (say)
Given that, side BA is produced to D such that BA = AD.
But we already have AB=AC.
Then, in ACD,AD=AC.So, ADC=ACD=2  (say)

In ABC,1+1+3=180(i)
In ADC,2+2+4=180(ii)
Also ,3+4=180    (Linear pair)
Adding (i) and (ii), we get2(1+2)+(3+4)=3602(1+2)=1801+2=90DCB=90


Mathematics

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