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Question

ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. BCD is equal to ____.


A

90

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B

45

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C

37

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D

Cannot be determined

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Solution

The correct option is A

90


Given, AB = AC and BA = AD.

In ABC,

ABC=ACB=x (angles opposite to equal sides)

In ACD,

ADC=ACD=y (angles opposite to equal sides)

BCD=x+y

In ABC,

ABC+ACB+BAC=180 (angle sum property of a triangle)

x+x+BAC=180

BAC=1802x

BAC+DAC=180 (Linear pair)

(1802x)+DAC=180

So, DAC=2x

In DAC,

DAC+ADC+ACD=180 (angle sum property of a triangle)

2x+y+y=180

2x+2y=180

x+y=90

BCD=BCA+ACD
= x+y
= 90

BCD=90


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