Question

in a parallelogram abcd,the angle bisectors of a and b meet at o . find angle aob

Answer 1

angle a +angle b= 180 (co interior)
1/2 angle a +1/2 angle b=90
so in triangle aob
angle aob+90=180
angle aob=90

HOPE IT HELPS!!

Answer 2

opposite angles of a parallelogram are supplementary
so
angle A+ angleB=180
divide both with 2
angle A/2+ angleB/2 = 90
angular bisector of A + angular bisector of B = 90
in triangle AOB
Sum of three sides is 180
WE KNOW THAT
\_OAB + \_OBA = 90
THEN
\_OAB + \_OBA+ \_AOB = 180
90 + \_AOB= 180
\_AOB= 180-90
\_AOB= 90