Sec 1-5
Concept: Describe Angle Pair Relationships
Objective: Given a pair of angles, use special
angle relationships to find angle measures.
Example 1
The Alamillo Bridge in Seville, Spain, was designed
by Santiago Calatrava. In the bridge, m<1=58° and
m<2=24°. Find the supplements of both <1 and <2
Suppl of <1. 180-58 =
122
Suppl of <2: 180 – 24 =
156
Example 2:
Find the supplement and complement of each angle
A. 38°
A. Comp: 52° Suppl: 142°
B. 172°
B. Comp: none Suppl: 8°
Example 3: Find the measure
of each angle
<P and <Z are complementary.
m<P = 8x - 7
and m<Z = x -11
m<P + m<Z = 90
8x-7 + x-11 = 90
9x -18 = 90
+18 +18
9x = 108
X=12
m<P = 8(12)-7
m<P = 89°
M<Z= (12)-11
=1
Example 4: Find the measure
of each angle
<P and <Z are Supplementary.
m<P = 8x + 100 and m<Z = 2x+50
m<P + m<Z = 180
8x+100 + 2x+50 = 180
10x+150 = 180
-150 -150
10x = 30
X=3
m<P = 8(3)+100
m<P = 124°
M<Z= 2(3)+50
= 56°
Example 5
Use the diagram to answer the
following questions
1. Are <1 and <2 a linear pair?
Yes
2. Are <4 and <5 a linear pair?
2
1
5
3
4
NO
3. Are <5 and <3 Vertical angles?
NO
4. Are <1 and <3 vertical <‘s?
YES
Example 6
<2 = 60°.Find the measure of the other angles
3
1
4
m<1= 60
2
m<2 = 60
m<3 = 120
m<4 = 120
Example 7 :
Find the measure of m<DEG and m<GEF
G
D
(7x3)۫
(12x-7)۫
E
(7x-3) + (12x-7) = 180
7(10)-3 = 67
19x-10 = 180
12(10)-7 =113
19x=190
X=10
F
Example 8:Find the measure of each angle
4x+15 + 5x+30 = 180
9x+45 = 180
4x+15
3y + 15
5x+30
-45 -45
9x = 135
4(15)+15 =
9
75
3y -15
X=15
9
5(15)+30 =
105
Example 8 cont.:Find the measure of each angle
3y+15 + 3y-15 = 180
6y = 180
4x+15
3y + 15
5x+30
6
6
y = 30
3y -15
3(30)+15 =
105
3(30)-15 =
75
Additional Slides:
• The following are Terms that you can
move and place where you like:
Adjacent Angles
2 angles are adjacent if they share a common
vertex
<DOS and
<SOG are
adjacent angles
D
S
O
G
Vertical Angles
 2 angles are vertical angles if their sides form two pairs
of opposite rays
4
1
3
2
<1 and <3 are vertical angles
<2 and <4 are vertical angles
Linear Pair
2 adjacent angles are a linear pair if their non-common
sides are opposite rays
5
6
<5 and <6 are a
linear pair
Complementary Angles
Two angles are Complementary if the sum of their
measures is 90°
30°
60°
1 2
<1 and <2 are complementary
Supplementary Angles
Two angles are Supplementary if the sum of their
measures is 180°
130°
50°
3 4
< 3 and <4 are
supplementary