Question

If the minor arc ac = 100 what is the measure of abc

Answer 1

If the minor arc AC measures 100 degrees, then we have the following;

`\begin{gathered} \text{ Minor arc+Major arc=360} \\ \text{Major arc=360-Minor arc} \\ \text{Major arc=360-100} \\ \text{Major arc=260} \end{gathered}`

The major arc measures 360 degrees as shown above.

Note that the angle formed by two tangents at the vertex is half of the angle formed at the circumference. Therefore we would have;

`\begin{gathered} \angle ABC=(1)/(2)Major\text{ arc} \\ \angle ABC=(1)/(2)*260 \\ \angle ABC=130 \end{gathered}`

Therefore, angle ABC measures 130 degrees.