2:6 Word Problems Involving Geometric Figures
Objective-To find missing angles and to solve word
problems involving geometric figures.
Some Strategies
1) Supplementary Angles
2) Complementary Angles
3) 180 Rule for Triangles
4) Vertical Angles
1
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
Supplementary Angles- Angles whose sum
is 180 .
a
b
ma + m b = 180
Find the value of x.
x + 30 = 180
- 30 - 30
x
30
x = 150
2
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
Find the supplement of the given angle.
1) 40
140
5) 89
91
2) 18
162
6) 23
157
3) 153
27
7) 131
49
4) 65
115
8) 118
62
3
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
Write a variable equation and solve.
Find an angle whose supplement
is 30 less than twice the angle.
x
2x - 30
x + (2x - 30) = 180
3x - 30 = 180
+30 +30
3x = 210
x = 70
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
70
4
Complementary Angles - Angles whose
sum is 90 .
b
a
ma + m b = 90
x
x + 40 = 90
- 40 -40
40
x = 50
5
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
Find the complement of...
1) 20
70
2) 47
43
3) 100
No complement
4) the supplement of 150
the complement of the supplement of 150
the complement of 30 =
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
60
6
Write a variable equation and solve.
Find an angle whose complement is 20
more than three times the angle.
x + 3x + 20 = 90
x
3x + 20
4x + 20 = 90
- 20 -20
4x = 70
4
4
x = 17.5
7
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
180 Rule for Triangles - the sum of the interior
angles of any triangle is
b
always 180 .
80
40
x
a
c
ma + m b + m  c = 180
40 + 80 + x = 180
120 + x = 180
x = 60
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
8
Find each angle below.
2y - 10
y + 14 = 63
2y - 10 = 88
y - 20 = 29
y +14
y - 20
(y + 14) + (2y - 10) + (y - 20) = 180
4y - 16 = 180
+16 +16
4y = 196
y = 49
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
180
9
Vertical Angles Theorem - the opposite angles
of intersecting lines
must be equal.
10
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
Vertical Angles Theorem - the opposite angles
of intersecting lines
must be equal.
11
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
Vertical Angles Theorem - the opposite angles
of intersecting lines
must be equal.
Find the missing angles a, b and c.
155 b 25
c
a
25
12
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
Vertical Angles Theorem - the opposite angles
of intersecting lines
must be equal.
Find the missing angles a, b and c.
155 b 25
c
a 155
25
13
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
Find the missing angle.
x
40
48
132
x = 180 - 40 - 48
x = 92
14
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
Find the missing angle.
119
61
124
56
x
x = 180 - 61 - 56
x = 63
15
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
Use a variable equation to solve.
1) The length of a rectangle is 5 less than
3 times its width. If the perimeter is 30 ft.,
find its dimensions.
3x - 5
2(x) + 2(3x - 5) = 30
2x + 6x - 10 = 30
+10 +10
Let x = width = 5
8x = 40
3x - 5 = length = 10
8 8
x=5
x
16
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
2) An angle is 6 degrees less than 3 times its
complement. Find the angle.
x
(3x - 6)
x + (3x - 6) = 90
4x - 6 = 90
+6 +6
4x = 96
4 4
x = 24
Let x = the complement = 24
3x - 6 = the angle = 3(24) - 6 = 66
17
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
3) The largest angle in a triangle is four times
the smallest. The third angle is 5 more than
twice the smallest. Find each angle.
n + (2n + 5) + 4n = 180
7n + 5 = 180
-5
-5
7n = 175
4n
2n + 5
7
7
n = 25
Let n = the smallest angle = 25
2n + 5 = the middle angle = 55
4n = the largest angle = 100
n
18
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
4) The lengths of the sides of a triangle are
consecutive even integers. If the perimeter
is 24 inches, find the length of each side.
x + (x + 2) + (x + 4) = 24
x
3x + 6 = 24
-6 -6
x+2
3x = 18
Let x = 1st side = 6 in.
3 3
x + 2 = 2nd side = 8 in.
x=6
x + 4 = 3rd side = 10 in.
x+4
19
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series