polygons – sum of the angles the sum of the interior angles of a convex polygon depends on the...
TRANSCRIPT
Polygons – Sum of the Angles
The sum of the interior angles of a convex polygon depends on the number of sides of the polygon. The formula is developed using triangles.
1802n where “n” is the number of sides
Polygons – Sum of the Angles
The sum of the interior angles of a convex polygon depends on the number of sides of the polygon. The formula is developed using triangles.
1802n where “n” is the number of sides
A triangle’s interior angles sum up to 180 degrees. By extending lines and connecting vertices in any polygon, we can divide that polygon into a certain number of triangles. We then multiply the number of triangles by 180 and that equals the sum of the interior angles in that polygon.
Polygons – Sum of the Angles
The sum of the interior angles of a convex polygon depends on the number of sides of the polygon. The formula is developed using triangles.
1802n where “n” is the number of sides
A triangle’s interior angles sum up to 180 degrees. By extending lines and connecting vertices in any polygon, we can divide that polygon into a certain number of triangles. We then multiply the number of triangles by 180 and that equals the sum of the interior angles in that polygon.
1
2
Square – two triangles
3601802
Polygons – Sum of the Angles
The sum of the interior angles of a convex polygon depends on the number of sides of the polygon. The formula is developed using triangles.
1802n where “n” is the number of sides
A triangle’s interior angles sum up to 180 degrees. By extending lines and connecting vertices in any polygon, we can divide that polygon into a certain number of triangles. We then multiply the number of triangles by 180 and that equals the sum of the interior angles in that polygon.
1
2
Square – two triangles
3601802 Pentagon – 3 triangles
5401803
1
2
3
Polygons – Sum of the Angles
The sum of the interior angles of a convex polygon depends on the number of sides of the polygon. The formula is developed using triangles.
1802n where “n” is the number of sides
A triangle’s interior angles sum up to 180 degrees. By extending lines and connecting vertices in any polygon, we can divide that polygon into a certain number of triangles. We then multiply the number of triangles by 180 and that equals the sum of the interior angles in that polygon.
1
2
Square – two triangles
3601802 Pentagon – 3 triangles
5401803
1
2
3
1
2
3
4
Hexagon – 4 triangles
7201804
Polygons – Sum of the Angles
The sum of the angles in a convex polygon depends on the number of sides of the polygon. The formula is developed using triangles.
1802n where “n” is the number of sides
EXAMPLE #1 : Find the measure of the interior angles of a polygon with 9 sides.
Now that you understand how the formula was developed, let’s try a few…
Polygons – Sum of the Angles
The sum of the angles in a convex polygon depends on the number of sides of the polygon. The formula is developed using triangles.
1802n where “n” is the number of sides
EXAMPLE #1 : Find the measure of the interior angles of a polygon with 9 sides.
Now that you understand how the formula was developed, let’s try a few…
12601807180291802n
Polygons – Sum of the Angles
The sum of the angles in a convex polygon depends on the number of sides of the polygon. The formula is developed using triangles.
1802n where “n” is the number of sides
EXAMPLE #1 : Find the measure of the interior angles of a polygon with 9 sides.
Now that you understand how the formula was developed, let’s try a few…
12601807180291802n
EXAMPLE #2 : Find the measure of the interior angles of a polygon with 16 sides.
Polygons – Sum of the Angles
The sum of the angles in a convex polygon depends on the number of sides of the polygon. The formula is developed using triangles.
1802n where “n” is the number of sides
EXAMPLE #1 : Find the measure of the interior angles of a polygon with 9 sides.
Now that you understand how the formula was developed, let’s try a few…
12601807180291802n
EXAMPLE #2 : Find the measure of the interior angles of a polygon with 16 sides.
2520180141802161802n
Polygons – Sum of the Angles
The sum of the angles in a convex polygon depends on the number of sides of the polygon. The formula is developed using triangles.
1802n where “n” is the number of sides
This formula also helps us find a missing angle in a polygon…
Polygons – Sum of the Angles
The sum of the angles in a convex polygon depends on the number of sides of the polygon. The formula is developed using triangles.
1802n where “n” is the number of sides
This formula also helps us find a missing angle in a polygon…
EXAMPLE # 3 : Find the measure of the unknown angle.
90° 90°
120°
?
Polygons – Sum of the Angles
The sum of the angles in a convex polygon depends on the number of sides of the polygon. The formula is developed using triangles.
1802n where “n” is the number of sides
This formula also helps us find a missing angle in a polygon…
EXAMPLE # 3 : Find the measure of the unknown angle.
90° 90°
120°
? 3601802180241802n
4 sides
Find the sum of interior angles…
Polygons – Sum of the Angles
The sum of the angles in a convex polygon depends on the number of sides of the polygon. The formula is developed using triangles.
1802n where “n” is the number of sides
This formula also helps us find a missing angle in a polygon…
EXAMPLE # 3 : Find the measure of the unknown angle.
90° 90°
120°
? 3601802180241802n
4 sides
60?
300360?
1209090360?
Subtract the sum of the given angles from the interior total…
Polygons – Sum of the Angles
Now let’s look at the exterior angles of a convex polygon. The exterior angles of ANY convex polygon ALWAYS add up to 360 degrees.
Polygons – Sum of the Angles
Now let’s look at the exterior angles of a convex polygon. The exterior angles of ANY convex polygon ALWAYS add up to 360 degrees.
Exterior angles are on the OUTSIDE of the polygon and are shown by extending the sides of the polygon.
Polygons – Sum of the Angles
Now let’s look at the exterior angles of a convex polygon. The exterior angles of ANY convex polygon ALWAYS add up to 360 degrees.
Exterior angles are on the OUTSIDE of the polygon and are shown by extending the sides of the polygon.
The angles created at each vertex are a pair that are supplementary.
So angles 1 and 2 add up to 180°.
1
2
Polygons – Sum of the Angles
Now let’s look at the exterior angles of a convex polygon. The exterior angles of ANY convex polygon ALWAYS add up to 360 degrees.
Exterior angles are on the OUTSIDE of the polygon and are shown by extending the sides of the polygon.
The angles created at each vertex are a pair that are supplementary.
So angles 1 and 2 add up to 180°.
Angles 3 and 4 add up to 180°.
1
2
34
Polygons – Sum of the Angles
Now let’s look at the exterior angles of a convex polygon. The exterior angles of ANY convex polygon ALWAYS add up to 360 degrees.
Exterior angles are on the OUTSIDE of the polygon and are shown by extending the sides of the polygon.
The angles created at each vertex are a pair that are supplementary.
So angles 1 and 2 add up to 180°.
Angles 3 and 4 add up to 180°.
Angles 5 and 6 add up to 180°.1
2
34
5
6
Polygons – Sum of the Angles
Now let’s look at the exterior angles of a convex polygon. The exterior angles of ANY convex polygon ALWAYS add up to 360 degrees.
Exterior angles are on the OUTSIDE of the polygon and are shown by extending the sides of the polygon.
The angles created at each vertex are a pair that are supplementary.
So angles 1 and 2 add up to 180°.
Angles 3 and 4 add up to 180°.
Angles 5 and 6 add up to 180°.
The exterior angles are #’s 2, 4, and 6
1
2
34
5
6
Polygons – Sum of the Angles
Now let’s look at the exterior angles of a convex polygon. The exterior angles of ANY convex polygon ALWAYS add up to 360 degrees.
Exterior angles are on the OUTSIDE of the polygon and are shown by extending the sides of the polygon.
The angles created at each vertex are a pair that are supplementary.
So angles 1 and 2 add up to 180°.
Angles 3 and 4 add up to 180°.
Angles 5 and 6 add up to 180°.
The exterior angles are #’s 2, 4, and 6
If the measure of angle 5 = 40 degrees…angle 6 = 140. Supplementary angles always add up to 180 degrees.
1
2
34
5
6