Sec 1-5Sec 1-5Sec 1-5Sec 1-5Concept: Describe Angle Pair Concept: Describe Angle Pair

RelationshipsRelationshipsObjective: Given a pair of angles, use Objective: Given a pair of angles, use

special angle relationships to find angle special angle relationships to find angle measures.measures.

Example 1The 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

A. 38°

B. 172°

A. Comp: 52° Suppl: 142°

B. Comp: none Suppl: 8°

Find the supplement and complement of each angle

Example 2:

<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

Make an

equation

Now find

each angle

measure

m<P = 8(12)-7

m<P = 89°

M<Z= (12)-11

= 1

Example 3: 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

Make an

equation

Now find

each angle

measure

m<P = 8(3)+100

m<P = 124°

M<Z= 2(3)+50

= 56°

Example 4: Find the measure of each angle

2

1 5

4

3

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?

NO

4. Are <1 and <3 vertical <‘s?

YES

Use the diagram to answer the following questions

Example 5

3

14

2

m<1= 60

m<2 = 60

m<3 = 120

m<4 = 120

<2 = 60°.Find the measure of the other angles

Example 6

Example 7 :Find the measure of m<DEG and m<GEF

(7x-3) + (12x-7) = 180

19x-10 = 180

19x=190

X=10

7(10)-3 = 67

12(10)-7 =113

(7x-3)۫ (12x-7)۫

D E F

G

4x+15

5x+303y + 15

3y -15

Use Linear Pairs to make

and equation

4x+15 + 5x+30 = 180

9x+45 = 180

-45 -45

9x = 135

9 9

X=15

Substitute x to find the angles

4(15)+15 =

75

5(15)+30 =

105

Example 8:Find the measure of each angle

4x+15

5x+303y + 15

3y -15

Use Linear Pairs to make

and equation

3y+15 + 3y-15 = 180

6y = 180

6 6

y = 30

Substitute y to find the angles

3(30)+15 =

105

3(30)-15 =

75

Example 8 cont.:Find the measure of each angle

Additional Slides:

• The following are Terms that you can move and place where you like:

Adjacent Angles

D

O

S

G

2 angles are adjacent if they share a common vertex

<DOS and <SOG are

adjacent angles

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

Linear Pair2 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°

<1 and <2 are complementary

30°

60°

1 2

Supplementary Angles

Two angles are Supplementary if the sum of their measures is 180°

130°50°

3 4

< 3 and <4 are supplementary