Question

Use the figure below to identify arcs and their measures. Complete the chart in the sketchpad

Answer 1

We can use the following definiotions to find our examples:

• An arc whose measure is less than 180 degrees is called a ,minor arc,.

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• An arc whose measure is greater than 180 degrees is called a ,major arc,.

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• An arc whose measure equals 180 degrees is called a ,semicircle,, since it divides the circle in two.

In this circle a major arc can be identified as BAD. We include the point A in the middle to indicate that the arc pass through it.

We can find its measure as:

`\begin{gathered} m\overarc{BAD}=m\overarc{BA}+m\overarc{AD} \\ m\overarc{BAD}=90\degree+(180\degree-50\degree) \\ m\overarc{BAD}=90\degree+130\degree \\ m\overarc{BAD}=220\degree \end{gathered}`

A minor arc can be expressed as BD. Its measure will be equal to:

`m\overarc{BD}=90\degree+50\degree=140\degree`

We can see that the sum of this two arc measures will be equal to the full circle measure (360°).

A semicircle can be identified as AC, and by definition will have a measure of 180°.

Then, we can complete the table as: