Intermediate Algebra (11th edition)

Find the measure of each angle in the triangles shown. See Example 4.

31. 32.

SECTION 2.4 Further Applications of Linear Equations 87

(x – 30)°

(^ x + 15)°

(2x – 120)°

1

2 (10x – 20)°

(x + 5)°

(x + 15)°

(9x – 4)°

(3x + 7)° (4x + 1)°

(2x + 7)°

(x + 61)°

x°

EXERCISES 33–36

FOR INDIVIDUAL OR GROUP WORK

Consider the following two figures. Work Exercises 33–36 in order.

RELATING CONCEPTS

2 x°

x° 60 °^60 ° y°

FIGURE A FIGURE B

33.Solve for the measures of the unknown angles in FIGURE A.

34.Solve for the measure of the unknown angle marked y° in FIGURE B.

35.Add the measures of the two angles you found in Exercise 33.How does the sum

compare to the measure of the angle you found in Exercise 34?

36.Based on the answers to Exercises 33–35,make a conjecture (an educated guess)

about the relationship among the angles marked 1 , 2 , and 3 in the figure shown

below.

1 3

2

In Exercises 37 and 38, the angles marked with variable expressions are called vertical angles.
It is shown in geometry that vertical angles have equal measures. Find the measure of each
angle.

37. 
    
    
    
    38. (7x + 17)°
    
    
    
    

(8x + 2)°

(9 – 5x)° (25 – 3x)°