Answer:
Each black pentagon in the soccer ball is surrounded by five white hexagons. Each white hexagon is, in turn, surrounded by three black pentagons and three other white hexagons. This pattern is repeated throughout the soccer ball.
To find the measures of the angles of the shapes that make the soccer ball, we need to first consider the angles of a regular pentagon and a regular hexagon.
A regular pentagon has five sides and five angles that are equal in measure. The formula for finding the measure of each angle in a regular pentagon is:
(angle measure) = (180(n-2))/n, where n is the number of sides.
In the case of a regular pentagon, n=5. Therefore, the measure of each angle in a regular pentagon is:
(angle measure) = (180(5-2))/5 = 108 degrees.
A regular hexagon has six sides and six angles that are equal in measure. The formula for finding the measure of each angle in a regular hexagon is:
(angle measure) = (180(n-2))/n, where n is the number of sides.
In the case of a regular hexagon, n=6. Therefore, the measure of each angle in a regular hexagon is:
(angle measure) = (180(6-2))/6 = 120 degrees.
Now, let's consider the angles of the shapes that make up the soccer ball.
Each black pentagon has five angles that are equal in measure. Therefore, each angle in a black pentagon measures:
(angle measure) = (180(5-2))/5 = 108 degrees.
Each white hexagon has six angles that are equal in measure. Therefore, each angle in a white hexagon measures:
(angle measure) = (180(6-2))/6 = 120 degrees.