Upon investigating, it is found that the number of triangles is always two less than the number of sides. This fact is stated as a theorem. The polygon in Figure 1 has seven sides, so using Theorem 39 gives:. An exterior angle of a polygon is formed by extending only one of its sides. The nonstraight angle adjacent to an interior angle is the exterior angle. The exterior angles of a regular pentagon are y, 2y, 3y, 4y, and 8y.
What is the size of the smallest interior angle of this pentagon? Learn Practice Download. Sum of Angles in a Polygon The sum of the angles in a polygon depends on the number of edges and vertices. Types of Polygons 2. Types of Angles in a Regular Polygon 3. Sum of Interior Angles in a Polygon 4. Sum of Exterior Angles in a Polygon 5.
Solved Examples 6. Practice Questions 7. So let's move on to the square, well right now we don't have any triangles but if I drew in one diagonal I've now created 2 triangles.
So the number of sides is 4, the number of triangles is 2 and if we have 2 triangles if I add that up that's going to be degrees. So I'm starting to notice a pattern let's make sure it works for a pentagon. Pentagon we can draw in 2 diagonals from one vertex and now we've created 1, 2, 3 triangles. So we have 5 sides we've created 3 triangles and 3 times is , so let's make this formula a little more general.
Let's say for an n sided polygon, the number of triangles that we're going to be able to draw is sum number. Well 3 minus 2 is 1, 4 minus 2 is 2, 5 minus 2 is 3, so you're taking the number of sides n and you're subtracting what number 2. Calculate the sum of interior angles in a pentagon. A pentagon contains 3 triangles.
The sum of the interior angles is:. The number of triangles in each polygon is two less than the number of sides. The formula for calculating the sum of interior angles is:.
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