Question

Parallel Lines and Angle Relationships

#1 What is the value of y. Type your answer below. *

#2 If the m<4 is 110 degrees, what is m<1 ? (Give number value only.) *

#3 If e || f and a || b, what is the value of y. *
A) 87
B) 88
C) 91
D) 92

Answer 1

1. y = 80°

2. m<1 = 70°

3. y = 92°

Explanation:

1. Since lines c and b are parallel lines cut across by transversal a, therefore:

y = 80° (alternate exterior angles are congruent)

2. m<1 is the supplement of m<4, because the angle that forms a linear pair with <1, corresponds with <4.

Therefore: m<1 = 180° - 110° = 70°

3. First, find the value of x.

(x + 1)° + (x - 3)° = 180° (supplementary)

x + 1 + x - 3 = 180°

2x - 2 = 180°

2x = 180 + 2 (addition property of equality)

2x = 182

x = 182/2 (division property of equality)

x = 91

(x + 1)° = y° (alternate interior angles are congruent)

Substitute x = 91

91 + 1 = y

92° = y