Exterior angle definitions
| Word backwards | roiretxe elgna |
|---|---|
| Part of speech | Noun. |
| Syllabic division | Ex-te-ri-or an-gle |
| Plural | The plural of the word "exterior angle" is "exterior angles." |
| Total letters | 13 |
| Vogais (4) | e,i,o,a |
| Consonants (6) | x,t,r,n,g,l |
Exterior angles of a polygon refer to the angles formed outside the polygon when one side is extended. These angles can provide valuable insight into the properties and relationships within the polygon.
Exterior angles are supplementary to the interior angles of a polygon, meaning that the sum of an exterior angle and its corresponding interior angle is always 180 degrees. This relationship can be helpful when analyzing the angles of a polygon.
Properties of Exterior Angles:
1. The measure of each exterior angle of a regular polygon is always the same.
2. The sum of the exterior angles of any convex polygon, regardless of the number of sides, is always 360 degrees.
Calculating Exterior Angles:
To find the measure of an exterior angle of a polygon, divide 360 degrees by the number of sides in the polygon. This will give you the measure of each exterior angle when the polygon is regular.
In irregular polygons, finding the measure of each exterior angle may require additional calculations or measurements, as the angles can vary in size depending on the shape of the polygon.
Understanding exterior angles and their properties can be essential in geometry and trigonometry, providing a foundation for more advanced mathematical concepts and problem-solving skills.
Exterior angle Examples
- In a triangle, the sum of the three exterior angles is always 360 degrees.
- When two parallel lines are cut by a transversal, the exterior angles on the same side are equal.
- To find the exterior angle of a regular polygon, divide 360 degrees by the number of sides.
- An exterior angle of a triangle can be calculated by subtracting the adjacent interior angle from 180 degrees.
- The exterior angle at a vertex of a polygon is formed by extending one side of the polygon.
- If two sides of a triangle are extended, the exterior angle formed will be equal to the sum of the two remote interior angles.
- The exterior angle of a regular pentagon is 72 degrees, as 360 degrees divided by 5 is equal to 72.
- When a line is drawn parallel to one side of a triangle, the exterior angles on opposite sides will be equal.
- An exterior angle of a quadrilateral can be found by summing the interior angles of the opposite triangle from the quadrilateral.
- In a cyclic quadrilateral, the exterior angle is equal to the interior opposite angle.