Download 8.1 Find angle measures in polygons Honors Geometry: Friday, 2-24

Honors Geometry: Friday, 2-24
8.1 Find angle measures in polygons
Diagonals "split up" a polygon into triangles
o
Each triangle has 180
Count up the triangles to calculate the
total interior degrees in each polygon
# of sides Polygon
3
4
5
6
7
8
9
10
n
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
n-gon
# of
1
s
total interior degrees
180
o
o
o
o
o
o
o
o
o
2
2(180 ) = 360
3
3(180 ) = 540
4
4(180 ) = 720
5
5(180 ) = 900
6
7
8
n-2
6(180 ) = 1080
o
o
7(180 ) = 1260
o
o
8(180 ) = 1440
o
(n-2)180
o
o
The coin shown is in the shape of a regular 11-gon.
Find the sum of the measures of the interior
angles.
What is the measure of each interior angle?
Identify the measurement for
S and
T
Examples:
1) The sum of the measures of the interior angles of a convex
o
polygon 1440 . Classify the polygon by the number of sides.
o
2) Each interior angle of a convex regular polygon is 150 .
How many sides are in this polygon?
Exterior angles:
Always, always, always 360°. No matter how many sides!!!
Identify the value for x and then find the missing angle
measurements.
8.1 Angle measures in polygons
Find the value of x in each picture below:
7. x = _________________
8. x = _________________
11. x = _________________
10. x = _________________
13.
I = ____________ E = ____________
9. x = _________________
12. x = _________________
14.
15.
I = ____________ E = ____________
I = ____________ E = ____________
16.
n = __________
17.
n = __________
18.
n = __________
n = __________
19.
Tell whether each statement is always, sometimes or never true.
20. As the number of sides of a polygon increases, the sum of the interior angles increases.
21. As the number of sides of a polygon increases, the sum of the exterior angles decreases.
22. If the number of sides of an equiangular polygon is doubled, the measure of each exterior angle is halved.
23. The measure of an exterior angle of a decagon is greater than the measure of an exterior angle of a pentagon.
24.
25.