Answer: The value of m∠ABC = 19 °
Step-by-step explanation:
Since we have given that
AC is tangent to the circle with center at B.
The measure of ∠ACB = 71°
And we know that "Radius is the shortest distance from the center to the tangent".
So, Radius is always perpendicular to the tangent.
So, the measure of ∠BAC = 90°
Consider, ΔABC, we get that
[tex]\angle ABC+\angle BAC+\angle ACB=180^\circ\\\\\angle ABC+90^\circ+71^\circ=180^\circ\\\\\angle ABC=180^\circ-90^\circ-71^\circ\\\\\angle ABC=19^\circ[/tex]
Hence, the value of m∠ABC = 19 °
