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Question

In an isosceles triangle AB=AC and BA is produced to D, such that AB=AD then BCD is


A

70°

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B

90°

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C

60°

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D

45°

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Solution

The correct option is B

90°


Step-1: Draw an isosceles triangle AB=AC and BA is produced to D, such that AB=AD.

In ABC,

AB=AC,

So, ABC=ACB.....(1) (Angles opposite to equal sides are equal)

AB=AD then, AC=AD
So, ACD=ADC.....(2) (Angles opposite to equal sides are equal)

Step-2: Find BCD

Adding (1)and (2)

ABC+ADC=ACB+ACD

ABC+ADC=BCD.....(3)

In BCD
ABC+BCD+BDC=180°

ABC+BDC=180°-BCD.....(4)

From (4) and (3)

180°-BCD=BCD

2BCD=180°

BCD=90°
Hence, BCD=90°

Hence, option (B) is the correct answer.


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