Question

In a triangle PRQ, side QR is extended to S. If angle PRS is 150 and RP=RQ, find the three angles of triangle PRQ

Answer 1

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Answer 2

$In \: a \: triangle \: PRQ , \: side \: QR \: is \\extended \: to \: S .$

$\angle {PRS} = 150\degree,\: and \: RP = RQ$

$i ) \angle {PRQ} + \angle {PRS} = 180\degree \\\blue { ( Linear \:pair )}$

$\implies \angle {PRQ} + 150\degree = 180\degree$

$\implies \angle {PRQ} = 180\degree - 150\degree\\= 30\degree$

$In \: triangle \: PRQ , \: RP = RQ$

$\implies \angle {RQP} = \angle {QPR}$

$\blue {( Angles \: opposite \:to \: equal \: sides )}$

$Now, \angle {RQP} + \angle {QPR} = \angle {PRS}$

$\blue { ( Sum \: of \: interior \: opposite}\\\blue { angles \: equal \: to \: exterior \:angles ) }$

$\implies \angle {RQP} + \angle {RQP} = 150\degree$

$\implies 2\angle {RQP} = 150\degree$

$\implies \angle {RQP} = \frac{150\degree}{2} \\= 75\degree$

Therefore.,

$\red { Three \: angles \: of \: the \: \triangle PRQ} \\\green { \angle {RQP} = \angle {QPR} = 75\degree \:and \angle {PRQ}= 30\degree }$

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