A. Solve:
1. What is the sum of the different measures of the exterior angles of a polygon with 99 sides?
2. What is the measure of the exterior angle of a regular octagon?
3. Three of the exterior angles of a hexagon have a sum of 240°. The remaining exterior angles are congruent to each other. Determine the measure of the remaining angles.
1. What is the sum of the different measures of the exterior angles of a polygon with 99 sides?
2. What is the measure of the exterior angle of a regular octagon?
3. Three of the exterior angles of a hexagon have a sum of 240°. The remaining exterior angles are congruent to each other. Determine the measure of the remaining angles.
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Answer:
1.The sum of the exterior angles of any polygon irrespective of the number of sides, or whether regular or irregular, is always 360 degrees.
It is only the sum of the interior angles of the polygon irrespective of the number of sides, that varies with the number of sides. The sum of the interior angles of the polygon that has 2312 sides = (2n-4)*right angles or (2x2312–4)*90 = (4624–4)*90 =4620*90 = 415800 degrees. The exterior angles (if the polygon is regular) will be 360/2312 = 0.155709342 degrees each, which you cannot measure by any physical means.
2.45°
A regular octagon has eight equal sides and eight equal angles. (a) Calculate the size of each exterior angle in the regular octagon. We do this by dividing 360° by the number of sides, which is 8. The answer is 360° ÷ 8 = 45°.
3.The exterior angles of a hexagon are the angles formed when we extend the sides of the hexagon. These angles have a total sum of 360°. If the hexagon is regular, we can simply divide the sum by 6 to get the measure of each exterior angle