In ? PQR PQ=PR,A is point in PQ and B is a point in PR,so that QR=RA=AB=BP
1. show that angle P:angle R=1:3
2.find the value of angle q

Hi, 
There must be show that angle P:angle Q=1:3 


left square bracket 1 right square bracket In space increment space PAB AB space equals space PB So space angle PAB space equals angle straight P angle ABR space equals space space angle PAB space plus angle straight P space space space left square bracket The space exterior space angle space of space straight a space triangle space is space the space sum space of space the space other space two space interior space angles right square bracket angle ABR space equals space space 2 angle straight P........... left parenthesis 1 right parenthesis In space increment space ABR AB space equals space AB So space angle ABR space equals angle ARB space equals space 2 angle straight P........... left parenthesis from space left parenthesis 1 right parenthesis right parenthesis angle BAR space plus space angle ARB space plus space angle ABR space equals 180 degree angle BAR space space equals 180 degree space minus space 4 angle straight P space............. left parenthesis 2 right parenthesis Sum space of space the space linear space pair space angles space is space 180 degree space space angle PAB space space plus space space angle BAR space space plus space angle QAR space space equals 180 degree space space angle straight P space plus space space 180 degree space minus space 4 angle straight P space space plus space angle QAR space space equals 180 degree.......... left parenthesis from space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis right parenthesis angle QAR space space equals 3 angle straight P.......... left parenthesis 3 right parenthesis In space increment space QAR AR space equals space QR So space angle QAR space equals angle straight Q space angle straight Q space equals 3 angle straight P.... left parenthesis from space left parenthesis 3 right parenthesis right parenthesis........... left parenthesis 4 right parenthesis left square bracket 2 right square bracket In space increment space PQR PQ space equals space PR angle straight Q space equals space angle straight R................. left parenthesis 5 right parenthesis angle straight P plus angle straight Q plus angle straight R space equals space 180 degree 1 third angle straight Q plus angle straight Q plus angle straight Q equals 180 degree space space space space space space space space space space left square bracket from space left parenthesis 4 right parenthesis space and space left parenthesis 5 right parenthesis right square bracket angle straight Q space equals space 77.14 degree

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