Line CB and Line CA are tangents to circle O at B and A.

Question

We can conclude that, for circle O, ∠BOA and ∠BCA are equal, complementary, or supplementary, and ∠BOC and ∠BCO are equal, complementary, or supplementary.

Please select one from each of the underlined.

Answer 1

They aren't equal. One is less than 90 degrees, the other > 90

They aren't complementary since one is >90 and to be complementary they have to sum to 90

That leaves only one choice: supplementary

Answer 2

2 triangles are congruent (they are right triangles - because tangent line is perpendicular to the radius; have the same hypotenuse, and one congruent leg = radius)

If you mark BOC as α and BCO as ß: α+ß=90 (two acute angles in the right triangle), so they are complimentary;

BOA is 2*α

BCA is 2* ß

So 2α+2ß=2(α+ß)=180 so they are supplementary