Question

Line BC is tangent to circle A at point B. If the measure of angle CAB is 43 degrees, the measure of angle BCA is ___ degrees.

Answer 1

The radius of a circle is perpendicular to a line that is tangent to the circle, it means that AB and BC are perpendicular, then Angle ABC measures 90°.

The measure of CAB is already given and we know that the sum of the interior angles of a triangle is 180 (triangle sum theorem), using this information we can find the measure of Angle BCA, this way:

$\begin{gathered} m\measuredangle ABC+m\measuredangle CAB+m\measuredangle BCA=180 \\ 90+43+m\measuredangle BCA=180 \\ m\measuredangle BCA=180-90-43 \\ m\measuredangle BCA=47 \end{gathered}$

The measure of angle BCA is 47 degrees.