The exterior angle of a regular polygon is the angle formed by an extended side and the adjacent side.
c) How do the central angel and the exterior angle of a regular pentagon compare? Is this relationship true in any regular polygon? Explain.
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You have posted several questions which are all based on the same principles
already pointed out by 'drwls'
Why don't you make a diagram of a regular polygon, sketch the 5 isosceles triangles created by joining the vertices to the centre.
Wouldn't the central angle of each of those be 360/5º ? or 72º ?
now work your way around the whole figure by finding all the angles, including the exterior angles formed by extending the sides
I noticed 'drwls' already pointed out that the exterior angle is 360/(number of sides), in this case 360/5
Isn't that the same as the central angle?
Now repeat the argument for an n-sided regular polygon.
You've received good ideas from two math teachers. Your other posts have therefore been removed.
If you have further questions, be sure to post what YOU HAVE DONE as well.
To understand the relationship between the central angle and the exterior angle of a regular polygon, we first need to understand what these angles represent.
1) Central Angle: The central angle of a regular polygon is the angle formed at the center of the polygon, with its vertex being the center point, and its sides coinciding with the radii of the polygon.
2) Exterior Angle: The exterior angle of a regular polygon is the angle formed by extending one side of the polygon and the adjacent side.
Now, let's consider a regular pentagon as an example.
A regular pentagon has 5 equal sides and 5 equal angles. Since it is a regular polygon, all the sides and angles are congruent.
Let's denote the interior angles of the pentagon as A, B, C, D, and E (starting from a vertex and moving clockwise). Since the sum of the interior angles of a polygon is given by the formula (n-2) * 180 degrees, where n is the number of sides of the polygon, for a pentagon, the sum of interior angles is (5-2) * 180 = 540 degrees.
Since all the interior angles of a regular polygon are equal, each angle of the pentagon measures 540 / 5 = 108 degrees.
Now, let's examine the relationship between the central angle and the exterior angle.
In a regular polygon, the exterior angle at each vertex is formed by extending one side and the adjacent side. For a pentagon, since it has 5 equal angles, each exterior angle measures 360 / 5 = 72 degrees.
On the other hand, the central angle of a regular polygon is formed by drawing a line from the center to each vertex. The central angle of a polygon can be found by simply dividing the full circle (360 degrees) by the number of sides in the polygon. For a pentagon, each central angle measures 360 / 5 = 72 degrees.
Hence, in a regular pentagon, the central angle and the exterior angle are equal, both measuring 72 degrees.
This relationship holds true for any regular polygon. In a regular polygon, both the central angle and the exterior angle will always be equal. The measure of each central angle is equal to the measure of each exterior angle, and both angles are determined by dividing the full circle (360 degrees) by the number of sides in the polygon.
So, to find the measure of both the central angle and the exterior angle of any regular polygon, you simply divide 360 degrees by the number of sides in the polygon.