In a parallelogram ABCD, the bisectors of the consecutive angles angleA and angleB intersect at P. Show that `angleAPB=90^(@)`.

If a quadrilateral ABCD, the bisector of angleC angleD intersect at O. Prove that angleCOD=(1)/(2)(angleA+angleB)

In the parallelogram ABCD if angleA = 65^(@) , find angleB, angleC and angleD .

In a parallelogram ABCD, angleDAB = 40^(@) find the other angles of the parallelogram.

If bisectors of angleA and angleB of a quadrilateral ABCD meet at O, then angleAOB is

In a cyclic quadrilateral ABCD, the bisectors of opposite angles A and C meet the circle at Pand Q respectively. Prove that PQ is a diameter of the circle.

Diagonal AC of a parallelogram ABCD bisects angleA . Show that (i) it bisects angleC alo (ii) ABCD is a rhombus.