Pa i r s o f A n g l Pa i r s o f A n g l e se s

1. Adjacent Angles

Two angles that share a common side and a common vertex, but do not overlap.

1. they have a common side: (line segment CB)

2. they have a common vertex: (point B)

In the figure shown, a and b are  adjacent angles.

They have a common vertexa common side

Angle ABC is adjacent to angle CBD

(.O)(Ray OA.)

They are NOT Adjacent Angles

They are NOT Adjacent Angles

They are NOT Adjacent Anglesangle PSQ and angle PSR overlap

they only share a side, not a vertex

they only share a vertex, not a side

They Adjacent Anglesthey share a vertex and a side

Which of the following are adjacent angles? Why?

          and           are adjacent angles. Find             , if                 and                 .

Solved Examples on Adjacent Angles

Choices:A. 90B. 26C. 80D. 16

Step1:              

Correct Answer : B

Solution:

Step 2: = 58 - 32 = 26

A

D

B

C

ExerciseExercises:s:Given: <DOC = 45; <BOA= 35; <COB = 42Given: <DOC = 45; <BOA= 35; <COB = 42

Find:Find:1.1. m<DOBm<DOB

m<COAm<COAm<DOAm<DOAm<DOC + m<BOAm<DOC + m<BOAm<DOB – m<BOAm<DOB – m<BOA

DDBB

CC

AAOO

1.1. m<DOB = 87m<DOB = 872.2. m<COA =77m<COA =773.3. m<DOA = 122m<DOA = 1224.4. m<DOC + m<BOA = 80m<DOC + m<BOA = 805.5. m<DOB – m<BOA = 52m<DOB – m<BOA = 52

Answers:Answers:

2. Complementary anglesTwo angles are complementary if their sum is 90° .

These two angles (40° and 50°) are Complementary Angles, because they add up to 90°.

                                            

 Notice that together they make a right angle.

These two are complementary because 27° + 63° = 90°

These two angles are complementary.                       

Sample Problems for Complementary Angles

1. If one angle is 60 degree find the measure of the other angle if the two angles are complementary to each other.

Sol :-   Since the two angles are complementary angles they must add up to 90 degree.So,   Angle 1 + Angle 2 = 90 degree

60 + angle 2 = 90 degree.Angle 2 = 90 – 60Angle 2 = 30 degrees

2. If one angle is 39 degree find the measure of angle 2 if the two angles are complementary to each other.

Solution:90 – 39 = 51

Angle 2 = 51 degrees.

3. Angle 1 measures 25 degrees and angle 2 measures 65 degrees. Are the angles complementary to each other?

Ans : Yes, They are complementary to each other

4. Find the complement angle of 40 degrees?

Solution:                                                          

40 + x = 90 x = 90 – 40 x = 50.The complementary angle is 50.

5. Find the measures of the complementary angle of the following:a. 22 degreesb. 63 degreesc. 45 degreesd. 75 degrees

      

1)      90-22=682)      90-3o=273)      90-45=454)      90-75=15

Solution:

5. Two complementary angles are A (x + 4)0 and B(2x – 7)0. Find the value of x and the measure of each angle.

2. Two complementary angles are the ratio 2 : 3, find these angles

ASSIGNMENT:

3. The two complementary angles are (4x + 8)° and (4x + 10)°. Find the value of x from the given data.

4. (10 – 3x)˚ and (90 – 2x)˚ are complimentary angles. Solve for x.

1. Find whether the angles 72 degree and 18 degree are complementary angles.

3. Linear pairTwo angles are a linear pair if they have a common side and their

If  angle 1  and  angle 2  are a linear pair, then angle1+ angle 2 = 180° .

other sides are opposite rays.

2. Supplementary anglesTwo angles are supplementary if their sum is 180° .

A linear pair is a pair of adjacent angles formed when two lines intersect.

angles 1 and 3.

Angles 1 and 2

angles 2 and 4,

angles 3 and 4,

Linear pairs are:

3. Linear pairTwo angles are a linear pair if they have a common side and their

4. Vertical anglesTwo angles are vertical angles iff the sides of one angle are opposite rays to the sides of the other.

Vertical angles are the "opposite angles" that are formed by two intersecting lines.

Note: If  Angle 1  and  angle 2  are vertical angles, then measure of angle 1 is equal to the measure of angle 2 .