Point O is the center of the circle on which points A, B, and C lie. It is known that ∠ABC = 15 ° and ∠OAB = 8 °. Find the angle BCO.

bystudin | May 31, 2020 | Education

Draw the segment OB.
Consider the triangle AOB.
Since AO = BO (these are the radii of a circle), this triangle is isosceles.
Therefore, ∠OAB = ∠ABO = 8 ° (by the property of an isosceles triangle)
∠OBC = ∠ABC-∠ABO = 15 ° -8 ° = 7 °.
The triangle BOC is also isosceles, because OB = OC (circle radii).
Therefore, ∠OBC = ∠BCO = 7 ° (by property).
Answer: 7.

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