Question

Ao and Bo are bisector of angle A and B respectively in a rhombus ABCD. Find angle AOB.

Answer 1

Answer:

∠AOB=90 degree

Step-by-step explanation:

in rhombus ABCD

∠OAB=1/2 of ∠DAB

and ∠OBA=1/2 of ∠CBA

now

∠DAB +∠CBA=180 DEGREE  .......interior angle

∴1/2 of ∠DAB + 1/2 of ∠CBA=90 degree

now in ΔAOB

∴1/2 of ∠DAB + 1/2 of ∠CBA +∠AOB=180

90+∠AOB=180

∴∠AOB=180 -90

∴∠AOB=90

Answer 2

Angle AOB is 90°.

AOB= 180 - 1/2(A+B)

and A + B = 180°,

so AOB =180 -1/2(180)

=180 - 90

= 90°.