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Son1ca
I got 180 because (although the picture is smaller and digital meaning I may be off) angle AOD = 85 degrees while angle BOC = 95. 95 + 85 = 180.
sqdancefan
The triangle formed by radii to the ends of a chord of a circle is an isosceles triangle. That means the central angle will be 180° less twice the base angle shown.
.. ∠AOB = 180° -2*35° = 110°
.. ∠COD = 180° -2*55° = 70°

Then the desired sum is
.. ∠AOD +∠BOC = 360° -110° -70° = 180° . . . . . . corresponds to selection A

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