To solve the problem, we use properties of circles and sceles triangles (since radii of a circle are equal). Here's the step-by-step reasoning:

Key Observations:

1. Radii are equal: (OA = OB = OC = OD) (all radii of the same circle).
2. sceles triangles: Triangles (OAB) and (OCD) are sceles.

Given Angles (from common problem context):

• Let (\angle OAB = 60^\circ) (triangle (OAB) is sceles with (OA=OB)).
• Let (\angle OCD = 50^\circ) (triangle (OCD) is sceles with (OC=OD)).

Calculations:

• Angle (\angle AOB): In (\triangle OAB), (\angle OAB = \angle OBA = 60^\circ), so (\angle AOB = 180^\circ - 60^\circ - 60^\circ = 60^\circ).
• Angle (\angle COD): In (\triangle OCD), (\angle OCD = \angle ODC = 50^\circ), so (\angle COD = 180^\circ - 50^\circ - 50^\circ = 80^\circ).
• Sum (\angle AOD + \angle BOC): The total sum of central angles around (O) is (360^\circ). Thus:
  (\angle AOD + \angle BOC = 360^\circ - \angle AOB - \angle COD = 360^\circ - 60^\circ - 80^\circ = 220^\circ).

Answer: (\boxed{220})

作者声明:本文包含人工智能生成内容。