Brian has been making octagonal wooden puzzles. He wants to make some hexagonal puzzles next. By how much does he needs to increase or decrease the angle measure on his template to make the hexagonal puzzles?
A. increase by 15 degrees
B. decrease by 15 degrees
C. increase by 35 degrees
D. decrease by 35 degrees
Octagon = 360o/8angles = 45o/angle,
Hexagon = 360o/6angles = 60o/angle.
60 - 45 = 15o Increase.
To determine the change in the angle measure on Brian's template, we need to calculate the difference between the angles of an octagon and a hexagon.
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.
To find the difference in angle measure between an octagon and a hexagon, we need to first determine the angle measure of each shape.
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.