Question

AC←→ is tangent to the circle with center at B.

The measure of ∠ACB is 71°.

What is the measure of ∠ABC?
Enter your answer in the box.
m∠ABC = __ °

Answer 1

I'm pretty sure the answer is "19", but if i'm wrong please don't kill me.

Answer 2

Answer: The value of m∠ABC = 19 °

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

`\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`

Hence, the value of m∠ABC = 19 °