Question

14 ) if the sum of the measures of the interior angles of a polygon is 9540°, how many sides does the polygon have? 180(n - 2) 180(n - 2) = 9540° 180n - 360 = 9540° + 360 + 360 180n = 9900° n = 55 sides 15 ) if the sum of the measures of the interior angles of a polygon is 2160°, how many sides does the polygon have? 180(n - 2) 180(n - 2) = 2160° 180n - 360 = 2160° + 360 + 360 180n = 2520 n = 14 sides 16 ) what is the sum of the measures of the interior angles of a 25 - gon? 180(25 - 2) = 180(23) = 4140 17 ) calculate the measure of each interior angle of the 25 - gon if each interior angle is congruent. (180(25 - 2))/25 = (180×23)/25 = 4140/25 = 165.6 18 ) complete the table using what we know about regular polygons. number of sides of the regular polygon n = 3, 4, 5, 6, 7, 8, 9 sum of the measures of the interior angles 180, 360, 900 measure of each interior angle 60, 180, 128.5 19 ) write a formula to calculate the measure of each interior angle if a regular polygon has n sides. 20 ) what is the measure of each interior angle of a regular 100 - sided polygon? 180(n - 2)/n 21 ) what is the measure of each interior angle of a regular 121 - gon? 22 ) if the measure of each interior angle of a regular polygon is equal to 150°, determine the number of sides. 180(n - 2)/n = 150 180(n - 2) = 150n 180n - 360 = 150n - 180n - 180n - 360 = - 30n - 360/-30 = -30n/-30 12 = n 23 ) if the measure of each interior angle of a regular polygon is equal to 171°, determine the number of sides. 180(n - 2)/n = 171 180(n - 2) = 171n 180n - 360 = 171n - 180n - 180n - 360 = - 9n - 360/-9 = -9n/-9 40 = n 24 ) if the sum of the measures of the interior angles of a polygon is 5940°, how many sides does the polygon have? 180(n - 2) = 5940 180n - 360 = 5940 + 360 + 360 180n = 6300 n = 35 sides 25 ) if the measure of each interior angle of a regular polygon is equal to 178.2°, determine the number of sides. 180(n - 2)/n = 178.2 180(n - 2) = 178.2n 180n - 360 = 178.2n - 180n - 180n - 360 = - 1.8n - 360/-1.8 = -1.8n/-1.8 200 = n sides

Explanation:

Answer:

1. \(55\)
2. \(14\)
3. \(4140^{\circ}\)
4. \(165.6^{\circ}\)
5. \(\frac{180(n - 2)}{n}\)
6. \(176.4^{\circ}\)
7. \(177.19^{\circ}\)
8. \(12\)
9. \(40\)
10. \(35\)
11. \(200\)