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Tatiana [17]
2 years ago
14

Find the measure of an interior angle and exterior angle of a regular 24gon

Mathematics
1 answer:
Julli [10]2 years ago
8 0

Answer:

Interior Angle: 165°

Exterior Angle: 15°

Step-by-step explanation:

So first you have to find the sum of all interior angles of a polygon with <u>24 sides</u>. This can be found using the formula:

sum = ( <em>n</em> - 2 ) * 180°     where '<em>n</em>' is the number of sides.

When '<em>n</em> = 24' then the sum is:

sum = ( 24 - 2 ) * 180°

Simplify and solve.

sum = 22 * 180°

sum = 3960°

Since there are 24 sides to the polygon, there are 24 interior angles. <u>Assuming that this polygon is equilateral</u>, you can surmise that:

<em>Interior Angle</em> = sum° / <em>n</em>   where n is the number of sides,

3960° / 24 = 165° = Interior Angle

Using that information, and combine it with the [Supplementary Angles Theorem] the exterior angle can be found by:

165° + x = 180°

Solve for x.

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