1. Concept: Describe Angle Pair Relationships
Sec 1-5
Concept: Describe Angle Pair Relationships
Objective: Given a pair of angles, use special angle relationships to find angle measures.

2. 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 < =
122
Suppl of <2: 180 – 24 =
156

3. Example 2: Find the supplement and complement of each angle A. 38°
B. 172°
A. Comp: 52° Suppl: 142°
B. Comp: none Suppl: 8°

4. Example 3: Find the measure of each angle
<P and <Z are complementary.
m<P = 8x - 7 and m<Z = x -11
Make an equation
m<P + m<Z = 90
8x-7 + x-11 = 90
9x -18 = 90
9x = 108
X=12
m<P = 8(12)-7
m<P = 89°
M<Z= (12)-11
= 1
Now find each angle measure

5. Example 4: Find the measure of each angle
<P and <Z are Supplementary.
m<P = 8x and m<Z = 2x+50
Make an equation
m<P + m<Z = 180
8x x+50 = 180
10x+150 = 180
10x = 30
X=3
m<P = 8(3)+100
m<P = 124°
M<Z= 2(3)+50
= 56°
Now find each angle measure

6. Example 5 Use the diagram to answer the following questions 2 3 1 4 5
1. Are <1 and <2 a linear pair?
Yes
2. Are <4 and <5 a linear pair? NO
3. Are <5 and <3 Vertical angles?
4. Are <1 and <3 vertical <‘s?
YES 2 1 5 4 3

7. Example 6 m<1= 60 m<2 = 60 m<3 = 120 m<4 = 120
<2 = 60°.Find the measure of the other angles
m<1= 60
m<2 = 60
m<3 = 120
m<4 = 120 3 1 4 2

8. Example 7 : Find the measure of m<DEG and m<GEF (12x-7)۫ (7x-3)۫
7(10)-3 = 67
12(10)-7 =113

9. Example 8:Find the measure of each angle
4x x+30 = 180
9x+45 = 180
9x = 135 9
X=15
Use Linear Pairs to make and equation
Substitute x to find the angles
4x+15
5x+30
3y + 15
3y -15
4(15)+15 = 75
5(15)+30 =
105

10. Example 8 cont.:Find the measure of each angle
3y y-15 = 180
6y = 180
y = 30
Use Linear Pairs to make and equation
Substitute y to find the angles
4x+15
5x+30
3y + 15
3y -15
3(30)+15 =
105
3(30)-15 = 75

11. Today's Work

12. Additional Slides:
The following are Terms that you can move and place where you like:

13. <DOS and <SOG are adjacent angles
2 angles are adjacent if they share a common vertex
<DOS and <SOG are adjacent angles D O S G

14. Vertical Angles
2 angles are vertical angles if their sides form two pairs of opposite rays 1 2 3 4
<1 and <3 are vertical angles
<2 and <4 are vertical angles

15. <5 and <6 are a 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

16. Two angles are Complementary if the sum of their measures is 90°
Complementary Angles
Two angles are Complementary if the sum of their measures is 90°
30°
60° 1 2
<1 and <2 are complementary

17. < 3 and <4 are supplementary
Supplementary Angles
Two angles are Supplementary if the sum of their measures is 180°
130°
50° 3 4
< 3 and <4 are supplementary