What is the angle created by two pentagons, if one side of each pentagon is glued together? Answer: 144
Plz explain the method.
an exterior angle of a pentagon is ... 360 / 5 = 72
two pentagons joined along one side form an angle of ... 2 * 72 = 144
To find the angle created by two pentagons, if one side of each pentagon is glued together, we need to use some geometrical concepts.
A regular pentagon has interior angles of 108 degrees. This means that each interior angle of a regular pentagon measures 108 degrees.
Since we are gluing together one side of each pentagon, we can think of it as merging two adjacent sides of each pentagon into one line segment. This forms a new shape, which can be visualized as a star shape with five arms. Each of these arms represents one of the sides of the original pentagons.
To find the angle created, we need to divide the star shape into five congruent triangles. Each triangle will have one angle located at the center of the star and two angles that form the arms of the star.
Since the interior angles of a triangle always sum up to 180 degrees, we can calculate the angle at the center of the star by subtracting the sum of the two arm angles (each measuring 108 degrees) from 180 degrees.
Angle at the center of the star = 180 degrees - (108 degrees + 108 degrees)
= 180 degrees - 216 degrees
= -36 degrees
However, angles cannot be negative, so we take the absolute value of -36 to get the positive value of 36 degrees.
Therefore, the angle created by two pentagons, if one side of each pentagon is glued together, is 36 degrees.