If the circle below has tangents AB and BC, and the measure of arc AC is 130 degrees, what is the measure of angle ABC?

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To find the measure of angle ABC when the arc AC measures 130 degrees, we can use the properties of tangents and arcs in a circle.

When two tangent lines intersect a circle, the angle formed between the two tangents (in this case, angle ABC) is equal to half the measure of the intercepted arc. Here, arc AC is the intercepted arc for angle ABC.

According to the given information, the measure of arc AC is 130 degrees. To find the measure of angle ABC, we can use the following formula:

Measure of angle ABC = (Measure of arc AC) / 2

Substituting the known value:

Measure of angle ABC = 130 degrees / 2

Calculating this gives:

Measure of angle ABC = 65 degrees

Therefore, the measure of angle ABC is 65 degrees.

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