Lines cb and ca are tangents to circle o at b and a. we can conclude that, for circle o, angle boa and angle bca are and angle boc and angle bco are

blank 1 options: equal, complementary, supplementary
blank 2 options: equal, complementary, supplementary

ANSWER

Angle BOA and angle BCA are supplementary

Angle BOC and angle BCO are complementary

EXPLANATION

The two tangents from an external point to a circle, will always meet two radii of the circle at an angle of 90°.

From the diagram, the external point, is C and the two radii are OA and OB.

The sum of angles in quadrilateral OABC is 360°.

This implies that,



We simplify to obtain,



This implies that;



Two angles that add up to 180 degrees are called SUPPLEMENTARY angles.

Similarly the sum of interior angles of triangle BCO is 180°.



This implies that,



.


Two angles that add up to 90° are COMPLEMENTARY angles.