Question

math unit 2 quiz: parallel lines version 1
name: thiago goncalves
use the picture to the right to answer questions 1 - 4.

1. which angles are vertical angles?

a. ∠1 and ∠2
b. ∠1 and ∠3
c. ∠1 and ∠4
d. ∠1 and ∠6

1. which angles are alternate exterior angles?

a. ∠2 and ∠7
b. ∠3 and ∠8
c. ∠1 and ∠8
d. ∠5 and ∠3

1. which angles are alternate interior angles?

a. ∠7 and ∠8
b. ∠6 and ∠3
c. ∠2 and ∠5
d. ∠1 and ∠4

1. which angles are corresponding angles?

a. ∠7 and ∠6
b. ∠1 and ∠4
c. ∠7 and ∠2
d. ∠1 and ∠8

1. in the diagram, k // j. what is the value of a?

a. 12
b. 24
c. 35
d. 73

1. in the figure m // n. which of the following is not true?

a. ∠3 = ∠6
b. ∠4 = ∠6
c. ∠1 = ∠7
d. m∠2 + m∠6 = 180

1. in the diagram, m // n. what is the value of x?

a. 3
b. 12
c. 28
d. 54

1. given that line m and n are parallel, find each of the following.

a. m∠1
b. m∠4
c. m∠7
d. m∠2

1. if m∠6 = 123 and m∠8 = 3(2x + 5), then solve for x and m∠5.

a. x =
b. m∠5 =

1. if m∠7 = 12x - 12 and m∠3 = 108, solve for x and m∠2.

a. x =
b. m∠2 =

1. in the figure below. ab // cd. match the following angle pairs to their vocabulary term.

a. alternate exterior angles
b. alternate interior angles
c. consecutive interior angles
d. corresponding angles
e. linear - pair angles
f. none of these angle pairs
g. same - side exterior angles
h. vertical angles

1. ∠1 and ∠8
2. ∠1 and ∠3
3. ∠8 and ∠5
4. ∠2 and ∠6
5. ∠2 and ∠8

Explanation:

Step1: Recall vertical - angles definition

Vertical angles are opposite each other when two lines intersect. For question 1, ∠1 and ∠4 are vertical angles, so the answer is C.

Step2: Recall alternate - exterior angles definition

Alternate exterior angles are outside the two parallel lines and on opposite sides of the transversal. For question 2, ∠2 and ∠7 are alternate exterior angles, so the answer is A.

Step3: Recall alternate - interior angles definition

Alternate interior angles are between the two parallel lines and on opposite sides of the transversal. For question 3, ∠2 and ∠3 are alternate interior angles, so the answer is C.

Step4: Recall corresponding angles definition

Corresponding angles are in the same relative position with respect to the parallel lines and the transversal. For question 4, ∠1 and ∠5 are corresponding angles, so the answer is B.

Step5: Use the property of parallel lines (k//j)

If k//j, then (8x - 4)=(4x + 36) (corresponding angles). Solve the equation 8x−4 = 4x + 36. Subtract 4x from both sides: 8x−4x−4=4x−4x + 36, 4x−4 = 36. Add 4 to both sides: 4x−4 + 4=36 + 4, 4x = 40. Divide both sides by 4: x = 10. So the answer for question 5 is A.

Step6: Analyze non - true statement for m//n

For parallel lines m//n, ∠2+∠6≠180 (∠2 and ∠6 are corresponding angles and are equal, not supplementary), so the answer for question 6 is D.

Step7: Use the property of parallel lines (m//n)

If m//n, then (6x + 26)=98 (corresponding angles). Solve the equation 6x+26 = 98. Subtract 26 from both sides: 6x=98 - 26, 6x = 72. Divide both sides by 6: x = 12. So the answer for question 7 is A.

Step8: Use the property of parallel lines (m//n)

If m//n, ∠1 = 130 (corresponding angles), ∠4 = 130 (vertical to ∠1), ∠7 = 50 (supplementary to ∠1), ∠2 = 50 (vertical to ∠7). So A. m∠1 = 130, B. m∠4 = 130, C. m∠7 = 50, D. m∠2 = 50.

Step9: Use the property of parallel lines (m//n)

If m//n, then ∠6=∠8. Given ∠6 = 123 and ∠8 = 3(2x + 5), set 123=3(2x + 5). Divide both sides by 3: 41=2x + 5. Subtract 5 from both sides: 2x=41 - 5, 2x = 36. Divide both sides by 2: x = 18. ∠5 is supplementary to ∠6, so m∠5=180 - 123 = 57. So A. x = 18, B. m∠5 = 57.

Step10: Use the property of parallel lines

If m//n, ∠7 and ∠3 are corresponding angles, so 12x−12 = 108. Add 12 to both sides: 12x=108 + 12, 12x = 120. Divide both sides by 12: x = 10. ∠2 is supplementary to ∠3, so m∠2=180 - 108 = 72. So A. x = 10, B. m∠2 = 72.

Step11: Match the angle - pairs

∠1 and ∠8: alternate exterior angles (A)
∠1 and ∠3: vertical angles (H)
∠8 and ∠5: alternate interior angles (B)
∠2 and ∠6: corresponding angles (C)
∠2 and ∠8: same - side exterior angles (G)

Answer:

1. C. ∠1 and ∠4
2. A. ∠2 and ∠7
3. C. ∠2 and ∠3
4. B. ∠1 and ∠5
5. A. 10
6. D. m∠2+m∠6 = 180
7. A. 12
8. A. m∠1 = 130, B. m∠4 = 130, C. m∠7 = 50, D. m∠2 = 50
9. A. 18, B. 57
10. A. 10, B. 72
11. ∠1 and ∠8: A, ∠1 and ∠3: H, ∠8 and ∠5: B, ∠2 and ∠6: C, ∠2 and ∠8: G