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Question

ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. What is the measure of BCD?


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Solution

Given, AB = AC and BA = AD

In ABC,

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

In ACD,

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

In BCD,

DBC+BCD+CDB=180

x+x+y+y=180

2x+2y=180

x+y=90

BCD=(x+y)=90

BCD=90


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