Transcript Polygon #of sides “n”

Chapter 11-Area of Polygons & Circles
Angle Measures in Polygons
Section 11.1
Goal –
To find the measures of interior and
exterior angles of polygons
Vocabulary Review
Convex polygon – A polygon that is not concave.
n- gon – A polygon that has many sides; specifically, n.
Regular polygon – A polygon that is equilateral and equiangular.
Polygon Interior Angles Theorem - 11.1
The sum of the measures of the interior angles of a convex n-gon is
(n – 2)180.
 m(int angles convex polygon)   n  2  180
Polygon
#of sides “n”
# of Δ’s
sum of int. angles
Triangle
3
1
1 x 180°
Quadrilateral
4
2
2 x 180°
Pentagon
5
3
3 x 180°
Corollary to Theorem 11.1
The measure of each interior angle of a regular n-gon is
180( n  2)
n
Example
Find x:
114°
105°
x°
135°
102°
Example
The meausre of each interior angle of a regular polygon is 140.
How many sides does this polygon have?
Polygon Exterior Angles Theorem - 11.2
The sum of the measures of the exterior angles of a convex polygon
is 360°.
2
1
3
5
4
m1  m2  m3  m4  m5  360
Corollary to Theorem 11.2
If the polygon is a regular n-gon, the measure of each
exterior angle is 360 (n = # of sides)
n
Example
Find: y
2y°
y°
y°
2y°
Example
Find: y
y°
Example
The meausre of each interior angle of a regular n-gon is 144.
Find n, the number of sides.