Opposite angles in any quadrilateral inscribed in a circle are supplements of each other. (Their measures add up to 180 degrees.)

angle AOC + angle ABC=180

130+angle ABC=180

angle ABC=180-130

angle ABC=50°

Answer:

∠ABC= 50°

Step-by-step explanation:

ABCO is a quadrilateral within the circle

∴∠AOC + ∠OCB +∠CBA + ∠BAO = 360°

also, ∠OAB = ∠OCB = 90° (radius of the circle is ⊥ to the circumference)

⇒ 130° + 90° + ∠ABC + 90° = 360°

⇒∠ABC + 310° = 360°

⇒∠ABC = 50°