Interior and Exterior angles of polygons

Summary

In this video, Mr. Ray explains how to calculate interior and exterior angles of polygons, focusing on regular and convex polygons. He demonstrates how the sum of interior angles increases with the number of sides and how to calculate it using the formula for triangles. For exterior angles, he explains that the sum is always 360° for any convex polygon. The video also highlights the relationship between interior and exterior angles, emphasizing their supplementary nature. Practical examples, like calculating angles for polygons with 12 or 18 sides, make the concepts easy to grasp for viewers.

Takeaways

• 😀 Regular polygons are polygons with all congruent angles and sides. Irregular polygons do not have this property.
• 😀 Concave polygons are 'dented,' meaning they have at least one angle greater than 180°, while convex polygons do not have dents.
• 😀 The sum of the interior angles of any polygon can be found by dividing the shape into triangles. The number of triangles is always two less than the number of sides.
• 😀 For a triangle, the sum of interior angles is 180°. For a quadrilateral, it is 360°. Each subsequent polygon's sum increases by 180° times the number of triangles.
• 😀 To find the sum of interior angles, count how many triangles can be formed by connecting the vertices and multiply by 180°.
• 😀 The sum of the exterior angles of any convex polygon is always 360°, regardless of the number of sides.
• 😀 Each exterior angle of a regular polygon is found by dividing 360° by the number of sides.
• 😀 Interior and exterior angles of a polygon are supplementary, meaning they always add up to 180°.
• 😀 When calculating the measure of one interior angle, finding the exterior angle first is often easier, then subtracting it from 180°.
• 😀 To calculate the number of sides in a polygon from the sum of the interior angles, divide the sum by 180° and add 2 to the result.

Q & A

What is the difference between a regular polygon and an irregular polygon?

A regular polygon has all congruent sides and angles, while an irregular polygon has sides and angles that are not equal.

What is the difference between concave and convex polygons?

A concave polygon has at least one interior angle greater than 180° and appears 'dented', while a convex polygon has all interior angles less than 180° and no dents.

How do you calculate the sum of the interior angles of a polygon?

The sum of the interior angles of a polygon can be calculated by the formula: (n - 2) * 180°, where 'n' is the number of sides.

What is the sum of the interior angles of a triangle?

The sum of the interior angles of a triangle is always 180°.

How do you find the sum of the interior angles for a quadrilateral?

A quadrilateral is made of two triangles, so the sum of its interior angles is 360°.

Why is the number of triangles in a polygon always two less than the number of sides?

The number of triangles in a polygon is always two less than the number of sides because a polygon can be divided into triangles by drawing diagonals from one vertex. For an n-sided polygon, the number of triangles is (n - 2).

What is the sum of the exterior angles of any polygon?

The sum of the exterior angles of any polygon, whether convex or concave, is always 360°.

How do you find the measure of one exterior angle of a regular polygon?

The measure of one exterior angle of a regular polygon can be found by dividing 360° by the number of sides (n). For example, for a regular polygon with 12 sides, the exterior angle would be 360° ÷ 12 = 30°.

What is the relationship between interior and exterior angles of a polygon?

Interior and exterior angles of a polygon are supplementary, meaning their sum is always 180°.

How do you find the number of sides of a polygon if you know the sum of its interior angles?

To find the number of sides, first divide the sum of the interior angles by 180° to determine the number of triangles in the polygon. Then, add 2 to this number to get the number of sides.