`PORS` is a parallelogram whose diagonals intersect at M. If `angleLPMS = 54^@, angleQSR=25^@ and angleSQR=30^@,` find :

PQRS is a parallelogram whose diagonals intersect at M. if anglePMS=54^(@),angleQSR=25^(@) and angleSQR=30^(@) , find: (i) angleRPS (ii) anglePRS (iii) anglePSR .

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If angleDBC=70^@, angleBAC " is " 30^@ , find angleBCD .

Diagonals of a parallelogram ABCD intersects at O. if angleBOC=90^@ and angleBDC=50^@ . Then find angleOAB .

The diagonals of a parallelogram ABCD intersect at O. If angleBOC=90^(@)andangleBDC=50^(@),"find"angleOAB.

Using vectors, prove that a parallelogram whose diagonals are equal is a rectangle.

In the figure above, MNOP is a parallelogram, diagonals MO and PN intersect at Q, angle OPQ=40^(@) and angleOMN=30^(@) . Find angleOQN .