1 Answer

Shkaper · Answer 1 · 2023-09-18T14:04:05+0000

SOLUTION

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:

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

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