The interior angles of a polygon add up to 1,800°. How many sides does it have? Give a reason for your answer.

Question

Mathematics

Jace Beck

3 August, 02:41

The interior angles of a polygon add up to 1,800°. How many sides does it have? Give a reason for your answer.

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Answers (1)

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Walker Arroyo · Answer 1

Hello!

To find the number of sides a polygon has given all the interior angles of this polygon added up to 1,800 degrees, we will need to use the formula of the sum of interior angles.

This formula is: total interior angles = (n - 2) 180°, where n is the number of sides.

Since we are given the "total interior angles", which is 1,800°, we can substitute that into our formula and solve for n.

1,800° = (n - 2) 180° (divide both sides by 180°)

10 = n - 2 (add 2 to both sides)

n = 12

Therefore, this polygon has 12 sides

Reasoning: To find the number of sides a polygon has, you need to use the formula: total interior angles = (n - 2) · 180°, where n is the number of sides. You would first substitute 1800° into the left side of the equation, and after solving this equation algebraically, you would be left with n = 12, which is 12 sides.