Question

На рисунке  AB=AC, AP=PQ=QR=RB=BC. Найдите угол A. 

Рисунок во влажениях. 

Answer 1

< - угол

< А = х =<AQP, <APQ = 180-x-x=180-2x

<RPQ = < PRQ = 180 - <APQ = 180 - (180-2x)=2x

< PQR = 180-2x-2x=180-4x

< RQB = 180 - <RQP - < AQP = 180 - (180-4x)-x = 3x = <RBQ

< QRB = 180 - <RQB - < RBQ = 180-3x-3x=180-6x

< CRB = RCB = 180 - <PRQ - <QRB = 180-2x - (180-6x)=4x

< RBC= 180 - <RCB - <CRB= 180 - 4x - 4x = 180-8x

< C = <B

<B = <RBC+<RBQ = 180 - 8x + 3x=180-5x

<C= 4x

4x = 180-5x

9x=180

x=20

<A=20