The sum of the measure of two complementary angle is equal to the 90 degrees.
Tt can conclude that, for circle O, angle BOA and angle BCA are __supplementary__, and angle BOC and angle BCO are __complementary__.
What is the theorem of two tangents from external point?
When the two tangent are drawn to a circle from an exterior point then according to this theorem-
- The length of these two tangents is equal.
- Both the tangents subtend equal angle at the center of the circle.
- The angle between the two tangent is bisect by the line joining to the exterior point and the center.
Given formation-
The center of the circle is O.
Lines CB and CA are tangents to circle O at B and A.
In the given properties of theorem of two tangents from external point is shown in the attached image below.
In the given image,
[tex]m\angle A=m\angle B=90^o[/tex]
In the quadrilateral OACB the measure of the angle is equal to the 360 degrees. Thus,
[tex]m\angle A+m\angle B+m\angle O+m\angle C=360^o\\90+90+m\angle O+m\angle C=360^o\\m\angle O+m\angle C=180^o[/tex]
As the sum of the measure of two supplementary angle is equal to the 180 degrees. Thus angle BOA and angle BCA are supplementary angles.
In the [tex]\Delta OBC[/tex] the angle OBC is equal to the 90 degrees and the sum of all the angles is equal to the 180 degrees for the triangle. Thus,
[tex]\angle BOC+\angle OBC+\angle BCO=180^o\\90+\angle OBC+\angle BCO=180^o\\\angle OBC+\angle BCO=90^o[/tex]
As the sum of the measure of two complementary angle is equal to the 90 degrees. Thus angle BOC and angle BCO are complementary angles.
Thus it can conclude that, for circle O, angle BOA and angle BCA are __supplementary__, and angle BOC and angle BCO are __complementary__.
Learn more about the theorem of two tangents from external point here;
https://brainly.com/question/8705027
