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Transcript
Pa i r s o f A n g l e s
1. Adjacent Angles
Two angles that share a common side and a common vertex, but do
not overlap.
Angle ABC is adjacent to angle CBD
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 vertex (.O)
a common side (Ray OA.)
Which of the following are adjacent angles? Why?
They Adjacent Angles
they share a vertex and a side
They are NOT Adjacent Angles
they only share a vertex, not a side
They are NOT Adjacent Angles
they only share a side, not a vertex
They are NOT Adjacent Angles
angle PSQ and angle PSR overlap
Solved Examples on Adjacent Angles
Find
and
, if
are adjacent angles.
Choices:
A. 90
B. 26
C. 80
D. 16
Solution:
Step1:
Step 2: = 58 - 32 = 26
Correct Answer : B
and
B
C
A
D
.
Exercises:
Given: <DOC = 45; <BOA= 35; <COB = 42
C
D
B
Find:
1.
m<DOB
m<COA
m<DOA
m<DOC + m<BOA
m<DOB – m<BOA
O
A
Answers:
1.
2.
3.
4.
5.
m<DOB = 87
m<COA =77
m<DOA = 122
m<DOC + m<BOA = 80
m<DOB – m<BOA = 52
2. Complementary angles
Two 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 – 60
Angle 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 degrees
b. 63 degrees
c. 45 degrees
d. 75 degrees
Solution:
1)
2)
3)
4)
90-22=68
90-3o=27
90-45=45
90-75=15
ASSIGNMENT:
1. Find whether the angles 72 degree and 18 degree are
complementary angles.
2. Two complementary angles are the ratio 2 : 3, find these angles
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.
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.
3. Linear pair
Two angles are a linear pair if they have a common side and their
other sides are opposite rays.
If angle 1 and angle 2 are a linear pair, then angle1+ angle 2 = 180° .
2. Supplementary angles
Two angles are supplementary if their sum is 180° .
3. Linear pair
Two angles are a linear pair if they have a common side and their
A linear pair is a pair of adjacent angles formed when two lines intersect.
Linear pairs are:
Angles 1 and 2
angles 3 and 4,
angles 2 and 4,
angles 1 and 3.
4. Vertical angles
Two 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 .