geometry

posted by .

What is the relationship between the measure of a central
angle of a polygon and the measures of an interior
and an exterior angle of the polygon?

  • geometry -

    It is important to specify that the following calculations apply to a regular polygon, of which all sides are equal in length, and all interior angles are equal.

    Denote the number of sides by n.

    The total of the central angles make up 360°, so each central angle is 360/n°.

    The exterior angle equals also 360/n°. Note that the exterior angle is the supplement of the interior angle, namely 180° - interior angle.

    The interior angle is therefore 180-exterior angle, and in terms of n, it is
    interior angle = 180 - 360/n

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math--fast help please

    Find the interior and exterior angle measurements of a polygon with this many sides: x=2y help?
  2. geometry

    What is the relationship between the measure of a central angle of a polygon and the measures of an interior and an exterior angle of the polygon?
  3. Geometry

    Any help would be greatful. What is the relationship between the measure of a central angle of a polygon and the measures of an interior and an exterior angle of the polygon?
  4. Geometry

    A regular polygon has an exterior angel measure of (x+3) Degrees and an interior angle measure of (13x-33) degrees Find the measure of each angle How mant sides does this polygon have?
  5. Geometry

    1. How many sides does a regular polygon have if one exterior angle is 90 degrees?
  6. geometry

    If the ratio of the interior angle to the exterior angle is 5:1 for a regular polygon, find a. the size of each exterior angle b. the number of sides of the polygon c. the sum of the interior angles d. Name the polygon
  7. Math

    1. The measure of an interior angle of a regular polygon is 20 more than thrice the measure of its adjacent exterior angle. Find the number of sides of the polygon and its total number of diagonals. 2. Find the sum and difference between …
  8. Math

    Are the statements Always, Sometimes or Never. Please explain why. Thanks. 1. An equilateral polygon is regular. 2. The greater the number of sides of a regular polygon, the smaller the measure of any of its exterior angle. 3. The …
  9. geometry

    Find the measure of each interior angle of a regular polygon whose central angle measures 60 degrees.
  10. geometry

    Find the measure of each exterior angle of a regular polygon whose central angle measures 120 degrees.

More Similar Questions