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If the sum of the interior angles of a polygon equals 2700 degrees, how many degrees are there in each interior angle of given polygon? What is the measure of each interior angle does a polygon have if the sum of its interior angles is 1800 degrees?

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User Orbnexus
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Final answer:

The sum of interior angles of a polygon is calculated by the formula (n-2) x 180, where 'n' is the number of sides. The polygons in the question have 17 and 12 sides respectively. If these polygons are regular, each interior angle would measure approximately 158.82 and 150 degrees respectively.

Step-by-step explanation:

In Mathematics, the sum of the interior angles of a polygon can be found using the formula (n-2) x 180, where 'n' is the number of sides of the polygon. If the sum of interior angles of a polygon is said to be 2700 degrees, we can set up the equation (n-2) x 180 = 2700, solve for 'n', and find that the polygon has 17 sides. However, it is important to note that this tells us the total degrees of all interior angles, not the measure of each individual interior angle.

If a polygon has a sum of interior angles of 1800 degrees, the same formula can be used, which would give us (n-2) x 180 = 1800. Solving this equation finds that the polygon has 12 sides.

In order to find the measure of each individual interior angle, you would have to know that the polygon is regular (meaning all sides and angles are equal). Then, you can divide the total degrees by the number of sides. For the first case, that would be 2700/17 ≈ 158.82 degrees. For the second case, it would be 1800/12 = 150 degrees.

Learn more about Interior Angles of a Polygon

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User Marco RS
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