Angle Pair

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Division of Pasig City and San Juan

SAGAD HIGH SCHOOL

E. Angeles St., Sagad Pasig City

STRATEGIC INTERVENTION MATERIALS

IN

MATHEMATICS III


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NENET M. PENARANDA

Head Teacher III - Math

LAZARO P. TORRES

Principal

LIGAYA G. INSIGNE

Education Supervisor I Secondary Math

Prepared and Submitted by:

FEMILA R. PALICAN

EDWIN P. PECO

HELEN U. RAYMUNDO


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ourney to the World of


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What have you observed on the figure

on the board ?

What kind of angles

are formed ?

The

figure

formeda pair

of

angles

Vertical

Angles are

formed by

intersectinglines


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EXPLORE:

Prepare a whole sheet of paper. You can

make a model of different pairs of angle by

folding a rectangular or square paper, byfolding it lengthwise, cross-wise and

diagonally. The folded corner provides a

convenient model of pair of angles.

From the model figure using a pieceof paper, the broken lines are the folded

crease on the paper. The pairs of angles are

a. supplementary angles

b. complementary angles

c. adjacent angles

d. linear pair

e. vertical angles


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In geometry, pairs of angles are related to each other in several ways. Some

examples are complementary angles, supplementary angles, vertical angles, adjacent

anglesand linear pair.

Two angles are called complementary angles if the sum of their degree measurements equals 90

degrees. One of the complementary angles is said to be the complementof the other.

ABCis the complement of CBD

Two angles are called supplementary angles if the sum of their degree measurements equals 180

degrees. One of the supplementary angles is said to be the supplementof the other.

ABCis the supplement of CBD
http://www.onlinemathlearning.com/pairs-of-angles.htmlhttp://www.onlinemathlearning.com/pairs-of-angles.htmlhttp://www.onlinemathlearning.com/pairs-of-angles.htmlhttp://www.onlinemathlearning.com/pairs-of-angles.htmlhttp://www.onlinemathlearning.com/pairs-of-angles.htmlhttp://www.onlinemathlearning.com/pairs-of-angles.htmlhttp://www.onlinemathlearning.com/pairs-of-angles.htmlhttp://www.onlinemathlearning.com/pairs-of-angles.htmlhttp://www.onlinemathlearning.com/pairs-of-angles.htmlhttp://www.onlinemathlearning.com/pairs-of-angles.htmlhttp://www.onlinemathlearning.com/pairs-of-angles.htmlhttp://www.onlinemathlearning.com/pairs-of-angles.html


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Two pairs of angles are formed by two intersecting lines. Vertical anglesare opposite angles in such an

intersection. Vertical angles are equal to each other.

Very often, math questions will require you to work out the values of angles given in diagrams byapplying the relationships between the pairs of angles.

Example 1: Given the diagram below, determine the values of the anglesx, y and z.

A B

O

C D

Solution:

Step 1:x is a supplement of 65.

Therefore,x+ 65=180x= 18065= 115

Step 2: zand 115are vertical angles.

Therefore, z= 115

Step 3: yand 65are vertical angles.

Therefore, y= 65

Answer:x= 115, y= 65and z= 115
http://www.onlinemathlearning.com/pairs-of-lines.htmlhttp://www.onlinemathlearning.com/pairs-of-lines.html


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Two angles which are adjacent and whose non common side are opposite rays and formed a

straight line are called linear pair.

D

DEF and DEG are linear pair

25 155

F E G

Two coplanar angles with a common side and a common vertex but, no common interior points.

HIJ and JIK are adjacent angles. H

j

I K


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1. Theorem 1 - 1 VERTICAL ANGLES vertical angles are congruent.

1 and 2 are vertical angles, show that 1 2.

* Angle Addition Postulate *1 m1 + m3 = 180, m2 + m3 = 180

3 4 by substitution, m1 + m3 = m2 + m3

2 Subtract m3 from each side you will get

m1 = m2, m1 m2 or 1 2.


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2. Theorem 1 - 2 If two angles are supplements of congruent angles, then the angles

are congruent.

1 2 3

1 and 2 are supplementary

3 and

2 are supplementaryshow 2 3

1 and 2 are supplementary, m1 + m2 = 180

3 and 2 are supplementary, m3 + m2 = 180

So m1 + m2 = m3 + m3

m1 = m3, m1 m3, 1 3


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3. Theorem 1 3 If two angles are complements of congruent angles, then the two

angles are congruent.

2

1 3

1 and 2 are complementary

3 and 2 are complementary

show 2 3

1 and 2 are complementary, m1 + m2 = 90

3 and 2 are complenmentary, m3 + m2 = 90

So m

1 + m

2 = m

3 + m

3 m1 = m3, m1 m3, 1 3


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1. 2.

1 2

1 2

3. 30 4.

150 50

40

Activity 1Identify the following pair of

angles


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b. Activity # 2

Find the measure of the following angles:

1. m1 = _______

m2 = _______

2

1 30

2. x = ___________

4x = __________

5x = __________5x 4x

x


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3.

x = ___________

1 m 1 = _________

(x + 10) 3 4 (4x 35) m 2 = _________ 2

m 3 = _________

m 4 = _________

4.

x = ____________

m1 = __________

(12x 7) 1 2 (3x - 8) m2 = __________


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5.

(4x + 5)

1

2 (3x + 8)

m 1 = ____________

m 2 = ____________


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c. Activity # 3

SOLVE:

1. The measure of a supplement of 1 is six times the

measure of a complement of 1. Find the measure of 1, its

supplement, and its complement.

2. A and B are supplementary angles andmA = 3x + 12 and mB = 2x 22. Find the measure of both

angles.

3. One angle is twice as large as its complement. Find

the measure of both angles.


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T

a. b.

3 1 2 4 P O Q

c. V

W Z

R S T


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X =

E C m1 = 2x + 6B m2 = 3x + 10

m3 = x + 20

mADE = 24x

3 1

2

D

A


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a.

x = _____, y = _____

1

(3x + 8 ) 2 3 (5x 20) m1 = ________

4 m2 = ________

(5x + 4y) m3 = ________

m4 = ________


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b.

m1 = _____________

2 m2 = _____________

1

25


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1.

2.


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A ti it C d


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Activity Card

Activity Card 1 Activity Card 3

1. Vertical Angle 1. m 1 = 72

2. Supplementary Angle, Linear Pair complement = 18

3. Supplementary Angle supplement = 108

4. Complementary Angle 2.. mA = 126

5. Adjacent Angle m B = 54

3. x, 2(90-x) Activity Card 2 x = 60 , complement = 30

1. m1=90 Assessment Card

m2=60 4. x = 2

2. x =18 m 1 = 10

4x =72 m 2 = 16

5x = 90 m 3 = 22

3. x=15 m

ADE = 48m1=155 Enrichment Card

m3=25 a. x = 14

m2=155 m 1 = 130

m4=25 m 2 = 50

4. x = 13 m 3 = 50

m 1 = 149 m 4 = 130

m 2 = 31 b. m 1 = 90

5. m 1 = 49 m 2 = 65m 2= 41

Activity 4

a. 1 and 3, 2 and 4 are supplementary, linear pair and adjacent

b. TOQ and QOV, QOV and VOP ,VOP and POT, POT and TOQ are allright angles and supplementary angles

c. WSZ and ZST are complementary angles while RSZ and ZST aresupplementary

.


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a. Geometry Activity Book for Enhancement

Skills by Ligaya G. Insigne

b. Geometry by Prentice Hall

c. Geometry by Edwin Moise

d. Geometry by Houghliton Mitten

e. Google and Mozila Firefox

Angle Pair

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