Question

∆PQR is isosceles in which PQ =QR . PS IS THE ALTITUDE.<Q=50°. Find the value of <RPS

Answer 1

Answer:

angle RPS=25°

Step-by-step explanation:

in triangle PQR,

PQ=QR

angle QRP=angle QPR=x

angle PQR +angle QRP +angle QPR=180°(angle sum

property)

50°+x+x=180°

50+2x=180°

2x=180-50=130°

x=130/2=65°

therefore, angle QRP=angle QPR=65°

in triangle PSQ,

angle PSQ=90° and angle SQP=50°

angle PSQ+angleSQP+angle SPQ=180°

90°+50°+angle SPQ=180°

140°+angle SPQ=180°

angle SPQ=180°-140°=40°

angle RPS=angle QPR-angleQPS

=65°-40°=25°