Question

What is the measure of ∠ABC ?

AC←→ is tangent to the circle with center at B. The measure of ∠ACB is 58°.

Answer 1

I think the answer is 32 degrees but i am not 100% sure

Answer 2

m∠ACB = 32°

Explanation:

It is given in the question that AC is tangent on a circle at A.

m∠ACB = 58° then we have to tell the measurement of ∠ABC.

In ΔABC, ∠BAC = 90° (since radius of a circle is always ⊥ to the tangent drawn)

Therefore in ΔABC

∠ABC + ∠BAC + ∠ACB = 180°

∠ACB + 90 + 58 = 180

∠ACB = 180 - (90 + 58) = 180 - 148 = 32°

Finally m∠ ACB = 32° is the answer.