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Question

The given figure shows a square ABCD and an equilateral triangle ABP. Calculate
PCD (in degrees)

181808_116908ececec4e0cacaa0cb4e5ea2c82.jpg

A
20o
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B
15o
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C
25o
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D
40o
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Solution

The correct option is C 15o
Given that ABCD is a square & APB is an equilateral triangle.
Hence PAB=BAO=ABP=BPA=60o[ All interior angles of equilateral triangle are equal to 60o]
So PBC=ABCABP=90o60o=30o
Since PB=AB=BC so PCB is a isosceles triangle.
So we get BCP=BPC[ Base angles of isosceles triangle are equal]
Now in PCB,
BPC+BCP+PBC=180o
2BCP+PBC=180o
2BCP+30o=180o
2BCP=180o30o
2BCP=150o
BCP=150o2
BCP=75o
Now PCD=BCDBCP
PCD=90o75o
PCD=15o

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