1. **State the problem:** We have three circle graphs with labeled sectors and arcs. We need to identify: a) Which label corresponds to a major arc? b) Which label corresponds to a minor sector? c) Which label corresponds to a major segment? 2. **Recall definitions:** - A **major arc** is an arc of a circle that is larger than a semicircle (greater than 180°). - A **minor sector** is a sector of a circle with an angle less than 180°. - A **major segment** is the larger region of a circle cut off by a chord, corresponding to the major arc. 3. **Analyze each graph:** - First circle graph: sectors labeled A (green) and B (yellow). Since sectors share the center, one is major and one is minor. Usually, the smaller sector is minor, the larger is major. - Second circle graph: sectors labeled C (blue) and D (pink). Same logic applies. - Third circle graph: arcs labeled E (orange, bottom left) and F (purple, top right). One arc is major, one is minor. 4. **Identify major arc:** - From the third graph, the larger arc is the major arc. The purple arc F is on the top right and appears larger than the orange arc E. - Therefore, **F** is the major arc. 5. **Identify minor sector:** - From the first graph, the smaller sector is the minor sector. The green sector A is smaller than yellow sector B. - Therefore, **A** is the minor sector. 6. **Identify major segment:** - A major segment corresponds to the major arc. From the third graph, the major arc is F, so the major segment is the region opposite the minor arc. - Since E is the minor arc, the major segment corresponds to the arc F. - But the question asks for the label of the major segment, which is the region bounded by the chord and the major arc. - The arcs are labeled, but segments are not explicitly labeled. However, since E is the minor arc, the segment opposite it (major segment) corresponds to arc E's chord and the larger arc F. - The major segment is associated with the arc F, but since only arcs are labeled, the major segment corresponds to the arc **E**'s chord and the major arc F. - Given the labels, the major segment is labeled **E** (orange arc) as it is the chord's minor arc, so the major segment is the region opposite E, which is the major segment. - Therefore, the major segment is labeled **E**. **Final answers:** - a) Major arc: **F** - b) Minor sector: **A** - c) Major segment: **E**