Download IM 1 Investigation 4.1.4A Name 1) Name each polygon and

IM 1
Investigation 4.1.4A
Name
1) Name each polygon and calculate the total sum of all the angles in the polygon.
a)
38mm
b)
66°
32mm
129°
142°
48mm
130°
40mm
27mm
100°
82mm
106°
92°
27mm
128°
40mm
127°
61mm
42mm
Name:
Name:
Angle Sum =
Angle Sum =
60°
32mm
c)
d)
45mm
29mm
80°
126°
135°
119°
29mm
135°
43mm
145°
34mm
124°
51mm
41mm
102°
37mm
108°
35mm
120°
113°
28mm
Name:
Name:
Angle Sum =
Angle Sum =
133°
39mm
2a) Split each of the following shapes into triangles by connecting from one vertex to each of the other nonadjacent vertices. Then count up the number of triangles created for each polygon and fill the answers in
the table below.
2b) How is the number of triangles related to the angle sum?
2c) Use the variables N = number of sides and S = Angle Sum.
Plot the points (N, S) on the graph and connect the points.
3a) Write a linear equation for the angle sum of a polygon
based on the number of sides.
3b) What is the slope?
Explain the meaning of the slope in this problem.
3c) Why is the value of the y-intercept not relevant to situation that the equation models?
4) Calculate the angle sum for each of the following polygons based on your formula. Show calculations.
a) Decagon (10 sides)
b) 15-sided polygon
c) 20-sided polygon
5) When the lengths of all of the sides of a polygon are equal, the polygon is called a regular polygon.
a) Were any of the polygons that you measured in problem #1 regular?
If so, which ones?
b) Look at the polygons in problem #2a. Do they appear regular?
Explain why.
6) When a polygon is regular, not only all the sides are equal, but so are all the angles. If you know that a
triangle is regular, and that the angle sum = 180°, how can you calculate the measure of each of the 3
angles? Explain in words and then calculate the answer.
Explain:
Measure of a single angle of a regular triangle =
Special name for the triangle:
7) If you know that a quadrilateral is regular, and that the angle sum = 360°, how can you calculate the measure
of each of the 4 angles? Explain in words and then calculate the answer.
Explain:
Measure of a single angle of a regular quadrilateral =
Special name for the quadrilateral:
In general to calculate the measure of each angle of a regular polygon, take the angle sum and divide by the
number of angles.
8) Calculate the measure of a single angle of each of the following polygons. Show calculations.
a) Pentagon
b) Hexagon
c) Heptagon
d) Decagon (10 sides)
e) 15-sided polygon
f) 20-sided polygon
9) Calculate the angle sum and the measure of a single angle of each polygon. Show calculations.
a) Octagon
b) 18-sided polygon
Angle Sum =
Angle Sum =
Single Angle =
Single Angle =