Please solve q 76 ?

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1 Answer
CW
May 15, 2018

#angleB=25 5/7#

Explanation:

enter image source here
Let #angleBCA=x, and angleABC=y#
Given #AB=BC, => angleBAC=angleBCA=x#
#=> color(red)(y+2x=180^@) ----- Eq(1)#
given #QB=QP, => angleQPB=y#,
given #AC=AP, => angleAPC=angleACP=x#
as #angleBPC=180^@, => angleQPA=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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