Given:
- Quadrilateral ABCD
- OA and OD are the bisectors of angle A and angle D, respectively

To prove:
- Angle AOD = 1/2(angle B + angle C)

Proof:
1. Angle AOB + Angle BOC = 180°:
- In quadrilateral ABCD, the sum of the interior angles is equal to 360°.
- Angles AOB, BOC, COD, and DOA form a linear pair, so their sum is equal to 180°.
- Therefore, angle AOB + angle BOC = 180°.

2. Angle AOD + Angle BOC = 180°:
- Similarly, angles AOD and BOC also form a linear pair, so their sum is equal to 180°.

3. Angle AOB = Angle COD:
- OA and OD are the angle bisectors of angles A and D, respectively.
- By definition, the angle bisector divides an angle into two equal angles.
- Therefore, angle AOB = angle COD.

4. Angle AOD = Angle BOC:
- From step 3, we know that angle AOB = angle COD.
- Rearranging the equation, we get angle COD = angle AOB.
- Since angle AOD + angle BOC = 180° (from step 2), and angle COD = angle AOB, we can substitute the values to get angle AOD + angle COD = 180°.
- Rearranging the equation, we get angle AOD = 180° - angle COD.
- Since angle COD = angle AOB, we can substitute the values to get angle AOD = 180° - angle AOB.
- Therefore, angle AOD = angle BOC.

5. Angle AOD = 1/2(angle B + angle C):
- From step 1, we know that angle AOB + angle BOC = 180°.
- Rearranging the equation, we get angle BOC = 180° - angle AOB.
- From step 4, we know that angle AOD = angle BOC.
- Substituting the value of angle BOC from the previous equation, we get angle AOD = 180° - angle AOB.
- Therefore, angle AOD = 1/2(angle B + angle C).

Conclusion:
- We have proved that angle AOD is equal to half the sum of angles B and C in quadrilateral ABCD when OA and OD are the bisectors of angles A and D, respectively.

yes ... because angle b+c will be 180° corresponding angles while angle b+d also 180° and bisected then 90° and angle aod =90°