Question

PR>PQ and PS bisects angle QPR. Prove that angle PSR > angle PSQ.

Answer 1

hope this will help you

Answer 2

$\huge\tt\red{GIVEN:-}$

$\small\tt{In\:∆PQR,}$

$\small\tt{(i)PR>PQ}$

$\small\tt{(ii)PS\:bisects\:\angle{QPR}=\angle{1}=\angle{2}}$

$\huge\tt\orange{TO\:PROVE:-}$

$\small\tt{(i)\angle{PSR}>\angle{PSQ}}$

$\huge\tt\purple{PROOF:-}$

$\small\tt{In\:∆PQS,}$

$\small\tt{By\:exterior\:angle\:property}$

$\small\tt{\angle{PSQ}=\angle{Q}+\angle{1}}$..........(1)

$\small\tt{In\:∆PSR,}$

$\small\tt{\angle{PSQ}=\angle{R}+\angle{2}}$..........(2)

$\small\tt{\angle{Q}+\angle{1}>\angle{R}+\angle{1}}$

$\small\tt{\angle{PSR}>\angle{PSQ}}$