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Geometry for Kids6 chapters | 45 lessons
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Nola has taught elementary school and tutored for four years. She has a bachelor's degree in Elementary Education, a master's degree in Marketing, and is a certified teacher.
Interior angles are angles inside of a shape. We find interior angles in triangles, quadrilaterals, and any other type of polygon. Interior angles can be acute like the angles in a diamond, obtuse like the angles in a hexagon, or right angles like those in a rectangle.
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A regular polygon is a shape in which all sides are equal and all angles are equal. A square is an example of a regular polygon because all sides of a square are the same length and all the angles are 90o. The hexagon in the diagram above is a regular polygon because all the sides and all the angles are equal.
The sum of the angles in a triangle always equal 180o. In a regular (or equilateral) triangle, all the sides and all the angles are equal. When all the angles are the same, we can divide the sum of the angles by the number of sides. The sum of the angles in a triangle is 180o and it has 3 sides: 180o/ 3 = 60o. All the angles in an equilateral triangle are 60o.
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Squares have 4 equal sides and the sum of the angles always equals 360o. This is easy to picture when you cut a square in half diagonally--it's made up of two triangles. If a triangle has an angle sum of 180o, it makes sense that, because there are two triangles in a square, the sum of the angles in a square is 360o (180o +180o).
To find the measurement of the interior angles in a square, you divide the sum of the angles (360o) by the number of sides (4). So, 360o / 4 = 90o. All the angles in a square are equal to 90o.
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The general rule is that every time you add another side to a shape, the sum of the angles increases by 180o. For example when you go from a 3-sided triangle (180o) to a 4-sided square, you add 180o to the sum of the angles. Therefore, a square has angles with a sum of 360o.
Likewise, if you add another side to a square and make it a pentagon (5 sides), you increase the sum of the angles by 180o. The sum of the angles of a pentagon is equal to 540o (360o +180o =540o).
The formula for this is (n-2) x 180o, where n is the number of sides of the shape. For example, a 10-sided figure would have an angle sum of (10-2) x 180o, or 1,440o.
Once you know the sum of the angles, you can calculate the measurement of the interior angles using the following formula: sum of angles / number of sides. For example, a pentagon has an angle sum of 540o and 5 sides. So, 540o / 5 = 108o. All angles in a pentagon are 108o. This formula works for all regular polygons, no matter how many sides they have.
Interior angles are angles inside of a shape. To calculate interior angles in regular polygons, take the sum of all the angles in the shape divided by the number of sides the shape has.
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Geometry for Kids6 chapters | 45 lessons
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