Given: In the given figure, ABC is a circle with center O.
Sides AB and OC are parallel and ∠AOC = 124°
So, the reflex angle AOC = 360° - 124° = 236°
To find: ∠BCO =?
Theorem: Angle subtended by an arc at the center of the circle is twice the angle subtended by the same arc at the remaining circumference of the circle.
Now, by applying the above theorem,
2×∠ABC = reflex angle AOC
or, ∠ABC = 236° ÷2 = 118° -------------(i)
Since sides AB and OC are parallel.
∠ABC + ∠BCO = 180° ------[ Sum of interior angles are supplementary]
or, ∠BCO = 180° - ∠ABC = 180° - 118° = 62°
Hence, the required angle ∠BCO will be 62° .