Question

25points for this question Given: AB ≅ BC and AO ≅ OC OK − angle bisector of ∠BOC Find: m∠AOK

Answer 1

• AB and BC are congruent (given)
• AO and OC are congruent (given)
• BO is congruent with itself (reflexivity)

Taken together, these three facts imply that triangles AOB and COB are congruent (side-side-side congruence postulate).

Now, it's not exactly clear whether A and C lie on the same line (it's possible that the figure is not drawn to scale). If they do, then both angles AOB and COB are right angles, so angle BOK has measure 45º, and so $m\angle AOK=135^\circ$.