9514 1404 393
Answer:
- arc RS = 100°
- RS is a minor arc
- arc ST = 80°
Step-by-step explanation:
The measure of an arc of a circle is the same as the measure of the central angle it subtends. That is, arc RS has the same measure as central angle RPS, which is marked as 100°.
Of course, the total of all central angles, hence all arcs, of a circle is 360°. A diameter of a circle cuts the circle in half, so each semicircle has a central angle measure and arc measure of 180°.
Any arc that is more than a semicircle is called a "major" arc. If it is less than a semicircle, it is a "minor" arc. Arcs RS and ST are minor arcs.
As always in geometry, the whole is the sum of the parts, so arcs RS and ST are supplementary. They total the measure of semicircle RST, which is 180°. Then ST = 180° -RS = 180° -100° = 80°.
__
<em>Additional comment</em>
Usually, an arc identified only by its end points is a minor arc. If the major arc is intended, then it will either be described as "major arc RS" or a point on the major arc will be given, as "arc RTS". The measure of arc RTS is 280°.
