Question 1131357: 2.) The sum of the interior angles of a regular polygon is 2340 degrees
Part A: Classify the polygon by the number of side
B: What is the measure of one interior angle of the polygon?
C: What is the measure of one exterior angle of the polygon?
3.) If the measure of an exterior angle of a regular polygon is 20 degrees, how many sides does the polygon have? Justify your answer.
5.) Given the regular heptagon and a regular hexagon
Part A: Which one has a greater angle? By how much is the angle greater?
B: Which one has a greater interior angle? By how much is the angle greater?
7.) The sum of the interior angles of a hexagon is equal to the sum of six consecutive rational numbers. What is the measure of the smallest interior angle of the hexagon.
Found 2 solutions by htmentor, greenestamps:
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! 2. Sum of interior angles of regular polygon = 2340
The sum of the interior angles of an n-sided polygon = 180(n-2).
Two examples are n = 3, equilateral triangle, S = 180 deg and n = 4, square, S = 360
2340 = 180(n-2)
n = 2340/180 + 2 = 15
The measure of one interior angle = 2340/15 = 156
The measure of one exterior angle = 360 - 156 = 204
3. If the exterior angle = 20, this implies an interior angle of 340 degrees.
Interior angles of polygons must be less than 180 degrees, so the polygon does not exist.
5. Heptagon has more sides and thus the larger interior angle
Heptagon: 180(7-2) = 900 -> Interior angle = 900/7 = 128.57
Hexagon: 180(6-2) = 720 -> Interior angle = 720/6 = 120
Greater by 8.57 deg
7. Let x = the smallest angle. 180(n-2) = 720 = x + x+1 + x+2 + x+3 + x+4 + x+5
180(n-2) = 6x + 15 = 720
x = 705/6 = 117.5
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Some of the answers from the other tutor are not right. An exterior angle of a polygon is 180 degrees minus the interior angle -- not 360 minus the interior angle.
2.A
To make calculations easier, I personally would change the given information to say that the sum of all the interior AND EXTERIOR angles is 2340+360 = 2700 degrees. Then that 2700 divided by 180 gives the number of sides in the polygon.
2700/180 = 15. The polygon has 15 sides.
2.C
The measure of an exterior angle is 360 degrees divided by the number of sides.
360-15 = 24. The measure of each exterior angle is 24 degrees.
2.B
The measure of an interior angle is 180 degrees minus the measure of an exterior angle.
180-24 = 156. The measure of each interior angle is 156 degrees.
3. In a regular polygon, the number of sides is 360 degrees divided by the measure of each exterior angle.
360/20 = 18. A regular polygon with exterior angles of 20 degrees has 18 sides.
5. (The other tutor's answers are fine for this one....)
7. This question can't be answered, because the statement of the problem has severe faults.
(1) The statement of the problem only says the sum of the measures of the interior angles is equal to the sum of "six consecutive rational numbers"; it doesn't say the six interior angles are those six consecutive rational numbers.
(2) There is no such thing as "six consecutive rational numbers". "six consecutive integers" makes sense; but there are no six consecutive integers with a sum of 720.
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