Basic Mathematics for College Students

State whether each of the triangles is an isosceles triangle.

See Example 2.

33. 
    
    
    
    34. 
        
    
    
    
    


34. 
    
    
    
    36. 
        
    
    
    
    

Find .See Example 3.

37. 
    
    
    
    38. 
        
    
    
    
    


38. 
    
    
    
    40. 
        
    
    
    
    

The degree measures of the angles of a triangle are represented

by algebraic expressions. First find. Then determine the measure

of each angle of the triangle.See Example 4.

41. 
    
    
    
    42. 
        
    
    
    
    


42. 
    
    
    
    44. 
        
    
    
    
    

Find the measure of the vertex angle of each isosceles triangle

given the following information.See Example 5.

45. The measure of one base angle is 56°.


46. The measure of one base angle is 68°.


47. The measure of one base angle is 85.5°.


48. The measure of one base angle is 4.75°.

x

x + 15° x + 15°

x

4 x

4 x

x

4 x – 5° x + 5°

x + 10° x

x + 20°

x

10°

y

45°

y

53 ° y

35 ° y

y

30°

60°

19° 143° 18°

45° 45°

78°

78°

24°

Find the measure of one base angle of each isosceles triangle

given the following information.See Example 6.

49. The measure of the vertex angle is 102°.


50. The measure of the vertex angle is 164°.


51. The measure of the vertex angle is 90.5°.


52. The measure of the vertex angle is 2.5°.

TRY IT YOURSELF

Find the measure of each vertex angle.

53. 
    
    
    
    54. 
        
    
    
    
    


54. 
    
    
    
    56. 
        
    
    
    
    

The measures of two angles of are given. Find the

measure of the third angle.

57. and ; find.


58. and ; find.


59. and ; find.


60. and ; find.


61. and ; find.


62. and ; find.


63. and ; find.


64. and ; find.
    In Problems 65–68, find.


65. 
    


66. 
    
    
    
    67. 
        
    
    
    
    

68.

5°

x

75°

x

86 °

x

x^156 °

x

m(A)4.5° m(B)128° m(C)

m(A)29° m(C)89.5° m(B)

m(B)67.25° m(C)72.5° m(A)

m(A)25.5° m(B)63.8° m(C)

m(B)33° m(C)77° m(A)

m(B)100° m(A)35° m(C)

m(A)45° m(C)105° m(B)

m(A)30° m(B)60° m(C)

ABC

47.5°

53.5°

33°

76 °

744 Chapter 9 An Introduction to Geometry