Download Name Date Period Patterns Worksheet: Polygon diagonals and

Name
Date
Period
Patterns Worksheet: Polygon diagonals and polygon angle measures
Number of diagonals in a polygon:
Number of
sides (n)
3
4
5
6
7
Number of
diagonals (d)
0
2
5
9
14
Sum of the angles in a polygon:
Formula:
d=
(
Number of
sides (n)
3
4
5
6
7
)
n n−3
2
Sum of all the
angles (a)
180º
360º
540º
720º
900º
Formula:
(
)
a = n − 2 180
A regular polygon is a polygon where all of the angles have the same size.
An isosceles triangle is a triangle with at least 2 angles that have the same measure.
1) Find the value of x in each figure below. Show your work.
a.
b.
111˚
c.
144˚
97˚
124˚
123˚
x˚
87˚
88˚
x˚
113˚
145˚
2x˚
87˚
98˚
x˚
2) If you have a regular 18-sided polygon: (show your calculations)
a) What is the sum of all the angles?
b) What is the measure of each angle?
c) How many diagonals does it have?
3) Find the value of x in the figure below. Justify your reasoning.
36˚
x˚
121˚
4) Triangle ABC is an isosceles triangle where angle A and angle B have the same measure. If angle
B is 42º, what is the measure of angle C? Draw a picture and show how you got your answer.
5) Polygon GHIJKL is a regular hexagon. Find the measure of angle HGI. Show how you got your
answer.
6) Create an octagon where 4 vertices are in each of the 4 quadrants and the other 4 vertices are on
the x and y axis. Identify each of the vertices.
Vertices:
10
9
8
7
6
5
4
3
2
1
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
2
3
4
5
6
7
8
9
10
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