Basic Mathematics for College Students

Refer to the figure below. Find the measure of each angle.
See Example 3.

69. 
    
    
    
    70. 
        
    
    
    
    


70. 
    
    
    
    72. 
        
    
    
    
    

First find .Then find and .See Example 4.

73. 
    
    
    
    74. 
        
    
    
    
    

First find .Then find and .See Example 4.

75. 
    
    
    
    76. 
        
    
    
    
    

Let represent the unknown angle measure. Write an equation
and solve it to find .See Example 5.

77. Find the complement of a 30° angle.


78. Find the supplement of a 30° angle.


79. Find the supplement of a 105° angle.


80. Find the complement of a 75° angle.

TRY IT YOURSELF

81. Refer to the figure in the next column and tell
    whether each statement is true. If a statement is
    false, explain why.
    a. has point Gas its endpoint.
    b. has no endpoints.
    c. has three endpoints.
    d. Point Dis the vertex of.
    e.
    f. AGF  BGE

m(AGC)m(BGD)

DGB

CD

·

AG

GF

¡

x

x

Q

P

Y

2 x + 35°

6 x − 5°

X

Z

4 x + 1 5 °

7 x − 60°

X

Y

P

Z Q

x m(ZYQ) m(PYQ)

6 x + 8° 4 x + 32°

A

B

C

D E

A

B

C

D E

2 x x + 30 °

x m(ABD) m(DBE)

M

O

Z

N

X T

1

70°

45°

2

Y

NYZ  2

 1 MYX

82. Refer to the figure for Problem 81 and tell whether
    each angle is an acute angle, a right angle, an obtuse
    angle, or a straight angle.
    a. b.
    c. d.
    Use a protractor to measure each angle.


83. 
    
    
    
    84. 
        
    
    
    
    


84. 
    
    
    
    86. 
        
    
    
    
    


85. Refer to the figure below, in which. Find
    the measure of each angle or sum of angles.
    a.
    b.
    c.
    d.


86. Refer to the figure below, in which
    , , and. Find the
    measure of each angle.
    a. b.
    c. d.

100 °

2

1

6

5

3 4

 3  6

 1  2

m(4)180° 3   4  4   5

m(1)m(3) 

2

4

1 3

m(2) m(4)

m(1)m(2)m(3)

 4

 3

m(1)50°

FGD BGA

AGC EGA

60 °

60 ° 30 °

30 °

90 °^90 °

D

B

F

C

A

E

G

9.1 Basic Geometric Figures; Angles 723