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Question

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

181807_58f55bcaea874b8095c38a6a1c2b3228.jpg
  1. 65o
  2. 85o
  3. 70o
  4. 75o

A
65o
B
70o
C
85o
D
75o
Solution
Verified by Toppr

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 BPC=BCP[ Base angles of isosceles triangle are equal ]
Now in PCB,
BPC+BCP+PBC=180o
2BPC+PBC=180o
2BPC+30o=180o
2BPC=180o30o
2BPC=150o
BPC=150o2
BPC=75o

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