Answer:
Therefore, the measure of angle ABC (∠ A B C) is 110 degrees.
Explanation:
In the given scenario, we have a circle with two chords, AC and BC. The measure of the arc AC is 60 degrees (A C ⌢ = 60) and the measure of the arc BC is 160 degrees (B C ⌢ = 160). We are asked to find the measure of angle ABC (∠ A B C).
In a circle, when two chords intersect, the measure of the angle formed at the point of intersection is equal to half the sum of the intercepted arcs.
Therefore, to find the measure of ∠ A B C, we need to find the sum of the intercepted arcs AC and BC, and then divide it by 2.
The intercepted arcs AC and BC together form the entire circumference of the circle, which is 360 degrees. So, we can set up the equation:
AC + BC = 360
Substituting the given measures:
60 + 160 = 360
220 = 360
Now, let's calculate the measure of ∠ A B C:
∠ A B C = (AC + BC) / 2
∠ A B C = 220 / 2
∠ A B C = 110 degrees
Therefore, the measure of angle ABC (∠ A B C) is 110 degrees.