Download Interior Angle Sums

Name: _________________________
Date: _______________________
Interior Angle Sums
1. Complete the chart by choosing one corner and drawing triangles to determine the sum
of the interior angles.
Diagram
Number
of sides
3
Sum of
interior angles
180
Understanding
The sum of the angles in any triangle
is 180o.
4
5
n
2. a) Determine the sum of the interior angles in a polygon with 15 sides. Show your
work.
b) Determine the number of sides in a polygon if the sum of the interior angles is
5400.
Show your work.
Name: _________________________
Date: _______________________
4. Derek is building a deck for his summer job in the shape of a regular octagon.
a) Define: regular octagon
?
b) Determine the measure of the interior angles of the deck.
Show your work.
5. A Canadian $1 coin, known as a loonie, is a regular polygon with 11 sides, called an
undecagon.
a) Define a regular polygon with 11 sides.
b) Determine the sum of the interior angles of the loonie.
c) What is the size of one of the interior angles?
Name: _________________________
1.
Date: _______________________
2a  a  90
3a  90
3a 90

3
3
a  30
2
.
2b  40  70
2b  110
2b 110

2
2
Name: _________________________
Date: _______________________
b  55
Name: _________________________
3
.
Date: _______________________
2b  3x  100
5x  100
5 x 100

5
5
x  20
4
.
4c  50  170
4c  50  50  170  50
4c  120
4c 120

4
4
Name: _________________________
Date: _______________________
c  30
Name: _________________________
5
.
Date: _______________________
5g  32  108
5g  32  32  108  32
5g  140
5g 140

5
5
g  28
Name: _________________________
Date: _________________________
Connecting Algebra to Geometry
1. a) The sum of the interior angles
in a triangle is:
b) An equation that models the
sum of the interior angles in
this triangle is:
c) Solve the equation to determine the value of x.
d) Use the value of x to calculate the size of:
W:
Y:
Z:
2. a) The sum of the angles in a right angle is:
b) Write 2 equations to model the sums of
the 2 sets of angles that add to 90º:
(i)
(ii)
c) Solve these equations to determine the values.
(i) solve for xº
(ii) solve for yº
d) Use the values of x and y to calculate the size of:
CBP:
ABQ:
Name: _________________________
Date: _________________________
3. Write an equation and solve for the unknown. State the theorem used to make the
equation.
a)
b)
c)
d)
e)
f)
g)
h)
Name: _________________________
i)
Date: _________________________
j)
i°
j°
2i°
75°
k)
l)
2k°
2l° + 20°
k°
2l°
l°
m)
n)
2n°
30°
80°
2k°
120°
3n°
Name: _________________________
Date: _________________________