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Answer :
The measure of the angle BCA, m∠BCA = 70°
The steps used to find the measure of the angle BCA are as follows;
The possible circle in the question, obtained from a similar question found through search created using MS Word is attached
Circle theorems states that the angle at the center of a circle is twice the angle at the circumference
The measure of the angle BOA = 250°
The measure of the angle at the circumference, BEA, m∠BEA = 125°
The measure of the interior angle, BOA of the quadrilateral BOAE is 360° - 250° = 110°
The radius of a circle is perpendicular to the tangent of the circle at the point of tangency, thus, m∠OBC = 90° and m∠OAC = 90°
The angle BCA in the quadrilateral OBCA is therefore; m∠BCA = 360° - 90° - 90° - 110°
360° - 90° - 90° - 110° = 70°
m∠BCA = 70°
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