1. The sum of the measures of the interior angles of a decagon (10 sided polygon) is 1,440. We found this by using the formula (n-2)(180). Thus, to find the measure of each interior angle we simply divide the sum by the number of total sides in the polygon. 1,440/10 = 144°.
2. N*60° = 360° [= sum of all exterior angles in a regular polygon]
or N = 360°/60° = 6 sides
3. An exterior angle of a triangle is equal to the sum of the two opposite interior angles. The sum of exterior angle and interior angle is equal to 180 degrees.
4. a pentagon, a 5-sided polygon. From vertex A we can draw two diagonals which separates the pentagon into three triangles. We multiply 3 times 180 degrees to find the sum of all the interior angles of a pentagon, which is 540 degrees.
5. SOLUTION: A regular polygon has an interior angle of 144 degree, calculate the number of sides polygon has. Since the interior angle is 144 degree, each exterior angle is 180 - 144 = 36 degrees. For any convex polygon (in particularly, for any regular polygon) the sum of exterior angles is 360 degrees. = 10 sides
6.We are given that each interior angle is 135∘, we have to find the number of sides of the polygon. Let's start with the assumption that the number of sides be n, this means that we have n sided regular polygon whose interior angle is 135∘. Therefore, we get the number of sides that the polygon has as 8.
7.Since the 15-gon is regular, this total is shared equally among the 15 interior angles. Each interior angle must have a measure of 2340 ÷ 15 = 156 degrees.
8. you can divide that by 12 to get the measure of each interior angle: 1800°/12 = 150°
9.The formula that gives the measure of the interior angle of a regular polygon is: (n-2)*180/n, where n is the number of sides. The measure of one angle of the regular polygon whose number of sides is 18, is of 160 degrees.
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Find the measure of one exterior angle of a regular polygon whose interior angles sun up to 6,660
Answers & Comments
Answer:
1. D. 144°
2. D. 6
3. 180°
4. C. 540
5. D. 10
6. D. 8
7. C. 156°
8. A. 150°
9. C. 160°
10.
Step-by-step explanation:
1. The sum of the measures of the interior angles of a decagon (10 sided polygon) is 1,440. We found this by using the formula (n-2)(180). Thus, to find the measure of each interior angle we simply divide the sum by the number of total sides in the polygon. 1,440/10 = 144°.
2. N*60° = 360° [= sum of all exterior angles in a regular polygon]
or N = 360°/60° = 6 sides
3. An exterior angle of a triangle is equal to the sum of the two opposite interior angles. The sum of exterior angle and interior angle is equal to 180 degrees.
4. a pentagon, a 5-sided polygon. From vertex A we can draw two diagonals which separates the pentagon into three triangles. We multiply 3 times 180 degrees to find the sum of all the interior angles of a pentagon, which is 540 degrees.
5. SOLUTION: A regular polygon has an interior angle of 144 degree, calculate the number of sides polygon has. Since the interior angle is 144 degree, each exterior angle is 180 - 144 = 36 degrees. For any convex polygon (in particularly, for any regular polygon) the sum of exterior angles is 360 degrees. = 10 sides
6. We are given that each interior angle is 135∘, we have to find the number of sides of the polygon. Let's start with the assumption that the number of sides be n, this means that we have n sided regular polygon whose interior angle is 135∘. Therefore, we get the number of sides that the polygon has as 8.
7. Since the 15-gon is regular, this total is shared equally among the 15 interior angles. Each interior angle must have a measure of 2340 ÷ 15 = 156 degrees.
8. you can divide that by 12 to get the measure of each interior angle: 1800°/12 = 150°
9. The formula that gives the measure of the interior angle of a regular polygon is: (n-2)*180/n, where n is the number of sides. The measure of one angle of the regular polygon whose number of sides is 18, is of 160 degrees.
( 6,660/180= 37 triangles 37+2= 39 360/39=9.23) 9.23