in a rhombus PQRS, angle RPQ= 54 degrees. find angle PRQ, PSR & RQS

Question

GEOMETRY OF A LEVELS

Answer 1

rhombus PQRS

draw diagonal PR

PQ=QR

angle RPQ=54º

triangle PQR is isosceles

angle PRQ=54º

angle RQP=180-54-54=72º

draw diagonal QS

diagonal QS bisects angle RQP

angle RQS=72º/2=36º

angle PSR=angle RQP (opposite angles of a rhombus are equal in measure)

angle PSR=72º