Question

Line BC Is a tangent to circle A at Point B. How would I find the measure of angle BCA? I need more explanation

Answer 1

Notice that line BA is a radius of the circle.

Since line BC is a tangen then the measure of angle ABC is:

`m\angle ABC=90^(\circ)`

Using Triangle Angle-Sum Theorem, it follows:

`m\angle ABC+m\angle BAC+m\angle BCA=180^(\circ)`

This gives:

`90^(\circ)+57^(\circ)+m\angle BCA=180^(\circ)`

Solving the equation gives:

`\begin{gathered} 147^(\circ)+m\angle BCA=180^(\circ) \\ m\angle BCA=180^(\circ)-147^(\circ) \\ m\angle BCA=33^(\circ) \end{gathered}`

Therefore the required answer is:

`m\angle BCA=33^(\circ)`