Given: AB ≅ BC , m∠MOC = 135° OM − angle bisector Prove: ∠ABO ≅ ∠OBC

Check attachment for the given triangle.

Proved

Step-by-step explanation:

Given m∠MOC = 135°

The sum of angles on a straight line is 180°, then

m∠MOC + m∠AOM = 180°

135° + m∠AOM = 180°

m∠AOM = 180° - 135° = 45°

Since OB bisects ∠AOC = 180°, they are perpendicular, and

∠AOB = 90°

Since OM bisects ∠AOB,

m∠AOM = m∠MOB = 45°

Since BO is perpendicular to AC m∠BOC = 90°

Triangle ABC is isosceles because AB ≅ BC.

BO bisects angle B , then

∠ABO ≅ ∠CBO

as required