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Question

# The given figure shows a square ABCD and an equilateral triangle ABP. Calculate the value of reflex ∠APC

A
2150
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B
1250
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C
2200
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D
2250
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Solution

## The correct option is D 2250Refer FigureGiven:ABCD is a squareABP is an equilateral triangleSolution:AB=BP=BC (△ABP is equilateral and AB and BC belong to a square, hence all are equal)∠ABC=∠ABP+∠PBC=60°+∠PBC90°−60°=∠PBC∠PBC=30°In △BPCBP=BC∠BPC=∠BCP=180−∠PBC2=150°2=75° ( angles opposite to equal sides of a triangle are equal)∠APC=∠APB+∠BPC=(60+75)°=135°Hence, Reflex ∠APC=(360−135)°=225°

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