Check attachment for the given triangle.
Answer:
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
