Mindbender #1 How many diagonals are in a nonagon? How many diagonals are in a nonagon? What is the sum of all the angles in an octagon? What is the sum.

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Presentation transcript:

Mindbender #1 How many diagonals are in a nonagon? How many diagonals are in a nonagon? What is the sum of all the angles in an octagon? What is the sum of all the angles in an octagon? What is the measure of one angle inside of a regular septagon? What is the measure of one angle inside of a regular septagon?

Solution: Nonagon has 9 sides. If n is equal to the number of sides, Nonagon has 9 sides. If n is equal to the number of sides, # diagonals = [n(n-3)] / 2 # diagonals = [n(n-3)] / 2 So, 9(9-3) / 2 = 9(6) /2 = 54/2 = 27 So, 9(9-3) / 2 = 9(6) /2 = 54/2 = 27 Therefore, there are 27 diagonals is a nonagon. Therefore, there are 27 diagonals is a nonagon.

Solution #2 The sum of all the angles in a polygon can be found using the formula: The sum of all the angles in a polygon can be found using the formula: (n-2)180 (where n is the # sides of the polygon). (n-2)180 (where n is the # sides of the polygon). In an octagon, there is 8 sides. (8-2)180 = 6(180) = 1,080 degrees. In an octagon, there is 8 sides. (8-2)180 = 6(180) = 1,080 degrees. All the angles inside of any octagon will add up to equal 1,080 degrees. All the angles inside of any octagon will add up to equal 1,080 degrees.

Solution #3 First, what is the sum of all the angles for any septagon? First, what is the sum of all the angles for any septagon? (n-2)180 = (7-2)180 (n-2)180 = (7-2)180 5(180) = 5(180) = 900 degrees. 900 degrees. Since it is regular, each of the angles are the same. All 7 angles will have an equal measure, so divide the total sum by 7 to find the angle measure of just one angle in the septagon— Since it is regular, each of the angles are the same. All 7 angles will have an equal measure, so divide the total sum by 7 to find the angle measure of just one angle in the septagon— 900 / 7 = degrees! 900 / 7 = degrees!

Mindbender #2 A B C D E F Suppose Hexagon ABCDEF is equilateral. CG = 3, GD = 4. ∠ BCD is congruent to ∠ AFE. Find the length of each side of the hexagon. What is the measure of ∠ F? What is the perimeter of Hexagon ABCGEF? G 140

Solution A B D E F G The hexagon’s angles must add up to equal 720. Already we have accounted for = 560. The remaining angles must then equal 720 – 560 = 160. Both of the two missing angles will be equal as it is given that they are congruent. 160/2 = 80 degrees. Thus, ∠ F = 80. We can find the measure of one side of the hexagon by applying the pythagorean theorem = x 2 So x 2 = 25  x = 5. The Hexagon is equilateral, which implies each side is 5. Then add all the lengths for the entire shape to find the perimeter: = 32.