What is the total measure of the exterior angles of a polygon with 6 sides?
What is the total measure of the exterior angles of a polygon with 6 sides?
The General Rule
| Shape | Sides | Sum of Interior Angles |
|---|---|---|
| Triangle | 3 | 180° |
| Quadrilateral | 4 | 360° |
| Pentagon | 5 | 540° |
| Hexagon | 6 | 720° |
How do you find the sum of the measures of the exterior angles?
Polygon Exterior Angle Sum Theorem
- If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360° .
- Consider the sum of the measures of the exterior angles for an n -gon.
- N=180n−180(n−2)
- Distribute 180 .
- N=180n−180n+360 =360.
What is the angle of a six sided shape?
720°
Does equal sides mean equal angles?
From this we learn that if two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is an isosceles triangle. We also know the converse: if two sides of a triangle are equal, their opposite angles are equal, and the triangle is isosceles.
What angles are equal in Triangle?
In a Euclidean space, the sum of angles of a triangle equals the straight angle (180 degrees, π radians, two right angles, or a half-turn). A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides.
What are the equal angles called?
Corresponding angles
What are opposite equal angles called?
The sides opposite to equal angles of a triangle are equal. Prove that if two angles of a triangle are congruent, then the triangle is isosceles.
What is an example of same side exterior angles?
When two parallel lines are cut by a third intersecting line, called a transversal line, eight angles are formed. In this figure, angles a and c are on the same side of the transversal line, so they have a same-side exterior relationship. Angles b and d also have a same-side exterior relationship.
Can interior and exterior angles be congruent?
Since alternate interior and alternate exterior angles are congruent and since linear pairs of angles are supplementary, same side angles are supplementary.