AC is tangent to the circle with center at B. The measure of ∠ACB is 71°.
What is the measure of ∠ABC?
+9466 m∠BAC = 90º
m∠ACB = 71º
m∠ABC + m∠ACB + m∠BAC = 180º
m∠ABC + 71º + 90º = 180º
Now just solve for m∠ABC.
m∠ABC = 180º - 71º - 90º
m∠ABC = 19º
+9519 If you construct a line from the center to any point on the circumference and construct a tangent on that line, the lines always are perpendicular.
Therefore ∠BAC = 90 degrees.
Therefore use the Angle Sum of Triangles:
90 + 71 + ∠ABC = 180
∠ABC = 19 degrees :)
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