gave me please the problemName of polygonNumber of SidesSum of interior angleMeasure of interior angleSum of exterior anglesMeasure of one exterior angles
Answer (1)
Answer:The problem you are referring to is probably a request for information about a specific polygon. Polygons are closed shapes with straight sides, and the names of polygons are typically based on the number of sides (vertices) they have. The sum of interior angles and the measure of interior angles can be calculated using formulas that are specific to each type of polygon. The sum of the measures of the interior angles of any polygon can be found by using the formula (n - 2) * 180°, where n is the number of sides. The measure of each interior angle can then be found by dividing this sum by the number of sides. For the sum of exterior angles, it is always 360° for any polygon, and the measure of one exterior angle is 360° divided by the number of sides.Here is a table with some common polygons and their properties:| Name of Polygon | Number of Sides | Sum of Interior Angles | Measure of Interior Angles | Sum of Exterior Angles | Measure of One Exterior Angle ||----------------|----------------|------------------------|--------------------------|------------------------|---------------------------|| Triangle | 3 | (3 - 2) * 180° = 180° | 180° / 3 = 60° | 360° | 360° / 3 = 120° || Quadrilateral | 4 | (4 - 2) * 180° = 360° | 360° / 4 = 90° | 360° | 360° / 4 = 90° || Pentagon | 5 | (5 - 2) * 180° = 540° | 540° / 5 = 108° | 360° | 360° / 5 = 72° || Hexagon | 6 | (6 - 2) * 180° = 720° | 720° / 6 = 120° | 360° | 360° / 6 = 60° || Heptagon | 7 | (7 - 2) * 180° = 900° | 900° / 7 = 128.57° | 360° | 360° / 7 = 51.43° || Octagon | 8 | (8 - 2) * 180° = 1080° | 1080° / 8 = 135° | 360° | 360° / 8 = 45° || Nonagon | 9 | (9 - 2) * 180° = 1260° | 1260° / 9 = 140° | 360° | 360° / 9 = 40° || Decagon | 10 | (10 - 2) * 180° = 1440°| 1440° / 10 = 144° | 360° | 360° / 10 = 36° || Dodecagon | 12 | (12 - 2) * 180° = 1800°| 1800° / 12 = 150° | 360° | 360° / 12 = 30° |For irregular polygons, the sum of the interior angles can be found using the same formula, but the measure of each interior angle would not be uniform. Instead, you would need to know the specific angles of each vertex to find the individual measures. For regular polygons, the interior angles are evenly distributed, which is why the measure of each interior angle can be calculated by dividing the sum of interior angles by the number of sides.
