Octagon = 360o/8angles = 45o/angle,
Hexagon = 360o/6angles = 60o/angle.
60 - 45 = 15o Increase.
A. increase by 15 degrees
B. decrease by 15 degrees
C. increase by 35 degrees
D. decrease by 35 degrees
Hexagon = 360o/6angles = 60o/angle.
60 - 45 = 15o Increase.
An octagon has 8 sides, which means each interior angle is calculated using the formula: (180 * (n-2)) / n, where n is the number of sides.
So, for an octagon, the interior angle measure is:
(180 * (8 - 2)) / 8 = 135 degrees.
To find the angle measure of a hexagon using the same formula:
(180 * (6 - 2)) / 6 = 120 degrees.
To determine the change in angle measure, we subtract the angle measure of the hexagon from the angle measure of the octagon:
135 degrees - 120 degrees = 15 degrees.
Therefore, Brian needs to decrease the angle measure on his template by 15 degrees.
The answer is: D. decrease by 15 degrees.
For an octagon, the total sum of the interior angles is given by the formula (n-2) * 180 degrees, where n is the number of sides. So for an octagon, with n = 8, the sum is (8-2) * 180 = 1080 degrees.
Since all angles in an octagon are congruent, we can divide the total sum by the number of angles to find the measure of each angle: 1080 degrees / 8 angles = 135 degrees.
For a hexagon, applying the same formula with n = 6 gives us a sum of (6-2) * 180 = 720 degrees. Dividing by the number of angles yields 720 degrees / 6 angles = 120 degrees per angle.
To find the difference between the two angle measures, we subtract the angle measure of the hexagon from the angle measure of the octagon: 135 degrees - 120 degrees = 15 degrees.
Therefore, Brian needs to decrease the angle measure on his template by 15 degrees to make the hexagonal puzzles.
The correct answer is: B. decrease by 15 degrees.