Download x 180° per triangle

Warm Up #1– An F-14 jet fighter and an FA-18 jet fighter/attack
aircraft each catapult off from the flight deck of the USS Harry S.
Truman. The F-14 immediately flies 50 miles east, then makes a 15°
turn toward the north and flies for another 40 miles. The FA-18 starts by
flying 40 miles south then makes a 25° right turn and flies another 50
miles. Draw and label a diagram, then determine which aircraft ends up
further from the aircraft carrier?
F  14
40
165
50
40
155
25
50
F/A 18
15
Warm Up #2– Find the range of possible values for x.
80
3x 15
51
47
80
5x  7
80
3x 15
51
47
80
5x  7
5x  7  3x 15 and 5x  7  0
2 x  7  15 and 5 x  7  0
2 x  8 and 5 x  7
x  4 and x   75
 75  x  4
Use a protractor to find the measure of each angle in each of the
following non-convex polygons. Then find the sum of these
interior angles
D
D
D
The Diagonal
A diagonal is a line that connects a
vertex of a polygon to any NON
ADJACENT vertex
Use a straight edge to draw all of the
diagonals from point D
D
D
D
D
Use the information from your polygons to
complete your interior angle sum theorem
chart.
The Polygon Interior Angle Sum Theorem
Triangle
3 Sides
Sum of Angles is 180°
1 Triangle
x 180° per triangle
180
The Polygon Interior Angle Sum Theorem
Quadrilateral
4 Sides
Sum of Angles is 360°
D
2 Triangles
x 180° per triangle
360
The Polygon Interior Angle Sum Theorem
Pentagon
5 Sides
Sum of Angles is 540°
D
3 Triangles
x 180° per triangle
540
The Polygon Interior Angle Sum Theorem
Hexagon
6 Sides
Sum of Angles is 720°
D
4 Triangles
x 180° per triangle
720
The Polygon Interior Angle Sum Theorem
n - gon
n Sides
(n – 2) Triangles
x 180° per triangle
 n  2 180
The Polygon Interior Angle Sum Theorem
The sum of the interior angles of an nsided convex polygon is:
 n  2 180
Exterior Angles
Remember that an exterior angle is the
angle formed by extending ONE side of
the polygon at each vertex.
exterior
angle
exterior
angle
exterior
angle
exterior
angle
Exterior Angles
Find the measure of each exterior angle
and the sum of the exterior angles of a
triangle, a quadrilateral, a pentagon, and
a hexagon
The Polygon Exterior Angle Sum Theorem
The sum of the exterior angles of an nsided convex polygon is:
360
Interior Angle Sum
Find the sum of the interior angles of a 9
sided convex polygon
n9
(n  2)180
 (9  2)180
 (7)180
 1260
Exterior Angle Sum
Find the sum of the exterior angles of a
15 sided convex polygon
360
A Regular Polygon
A regular polygon is a polygon with
equal length sides and equal measured
angles
Regular Polygon Angles
Find the measure of each exterior angle
of a regular decagon
n  10
Sum of Exterior Angles  360
360
Each Exterior Angle 
10
Each Exterior Angle  36
Regular Polygon Angles
Find the measure of each interior angle
of a regular 15 sided convex polygon
n  15
Sum of Interior Angles  15  2180  2340
2340
Each Interior Angle 
15
Each Interior Angle  156
Regular Polygon Angles
The measure of each exterior angle of a
regular polygon is 30°. How many sides
does the polygon have?
Sum of Exterior Angles  360
30n  360
n  12
The polygon has 12 sides
Regular Polygon Angles
The measure of each interior angle of a
regular polygon is 162°. How many
sides does the polygon have?
Sum of Interior Angles  162n
Sum of Interior Angles  (n  2)180
 n  2180  162n
180n  360  162n
18n  360
n  20
The polygon has 20 sides
Regular Polygon Angles
The measure of each interior angle of a
regular polygon is 162°. How many
sides does the polygon have?
If each interior angle is 162
then each exterior angle is 18
Sum of Exterior Angles  360
18n  360
n  20
The polygon has 20 sides