Please solve q 76 ?

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1 Answer
CW
May 15, 2018

angleB=25 5/7∠B=2557

Explanation:

enter image source here
Let angleBCA=x, and angleABC=y∠BCA=x,and∠ABC=y
Given AB=BC, => angleBAC=angleBCA=xAB=BC,⇒∠BAC=∠BCA=x
=> color(red)(y+2x=180^@) ----- Eq(1)⇒y+2x=180∘−−−−−Eq(1)
given QB=QP, => angleQPB=yQB=QP,⇒∠QPB=y,
given AC=AP, => angleAPC=angleACP=xAC=AP,⇒∠APC=∠ACP=x
as angleBPC=180^@, => angleQPA=180-x-y=x∠BPC=180∘,⇒∠QPA=180−x−y=x
In DeltaPAQ, x+4y=180^@,
=> 2x+8y=360^@ ------ Eq(2)
Subtracting Eq(1) from Eq(2), we get,
7y=180, => y=180/7=25 5/7

Hence, angleB=y=25 5/7

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