Question

quiz - parallel lines and transversals
name: tyshawn daniels
date:
relate properties of angles formed by parallel lines and transversals. (standard g.gco.8)

1. ∠3 and ∠5 are

a. same - side interior angles
b. corresponding angles
c. alternate interior angles
d. alternate exterior angles

1. ∠7 and ∠2 are

a. same - side interior angles
b. corresponding angles
c. alternate interior angles
d. alternate exterior angles

1. ∠5 and ∠4 are

a. same - side interior angles
b. corresponding angles
c. alternate interior angles
d. alternate exterior angles

1. ∠4 and ∠8 are

a. same - side interior angles
b. corresponding angles
c. alternate interior angles
d. alternate exterior angles

1. if m∠4 = 150°. find the value of ∠3

a. m∠3 = 150°
b. m∠3 = 30°
c. m∠3 = 120°
d. ∠3 cannot be found

1. if m∠7 = 45°. find the value of ∠2

a. m∠2 = 135°
b. m∠2 = 90°
c. m∠2 = 45°
d. m∠2 cannot be found

1. name a pair of corresponding angles.

a. <7 and <2
b. <8 and <6
c. <5 and <6
d. <3 and <7

1. name a pair of same - side interior angles.

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

1. name a pair of alternate exterior angles.

a. <1 and <8
b. <8 and <6
c. <3 and <6
d. <8 and <4

1. find m∠6

a. 40°
b. 50°
c. 90°
d. 140°

Explanation:

Step1: Recall angle - pair relationships

When two parallel lines are cut by a transversal, we use the following angle - pair properties:

• Same - Side Interior Angles are supplementary (sum to 180°) and are on the same side of the transversal and between the parallel lines.
• Corresponding Angles are congruent and are in the same relative position with respect to the parallel lines and the transversal.
• Alternate Interior Angles are congruent and are between the parallel lines and on opposite sides of the transversal.
• Alternate Exterior Angles are congruent and are outside the parallel lines and on opposite sides of the transversal.

Step2: Solve question 1

∠3 and ∠5 are Same - Side Interior Angles since they are on the same side of the transversal and between the parallel lines. So the answer is A.

Step3: Solve question 2

∠7 and ∠2 are Alternate Exterior Angles as they are outside the parallel lines and on opposite sides of the transversal. So the answer is D.

Step4: Solve question 3

∠5 and ∠4 are Alternate Interior Angles as they are between the parallel lines and on opposite sides of the transversal. So the answer is C.

Step5: Solve question 4

∠4 and ∠8 are Corresponding Angles as they are in the same relative position with respect to the parallel lines and the transversal. So the answer is B.

Step6: Solve question 5

If m∠4 = 150°, and ∠4 and ∠3 are a linear - pair (sum to 180°), then m∠3=180° - 150° = 30°. So the answer is B.

Step7: Solve question 6

If m∠7 = 45°, and ∠7 and ∠2 are Alternate Exterior Angles, then m∠2 = 45°. So the answer is C.

Step8: Solve question 7

A pair of corresponding angles is ∠3 and ∠7. So the answer is D.

Step9: Solve question 8

A pair of Same - Side Interior Angles is ∠5 and ∠3. So the answer is C.

Step10: Solve question 9

A pair of alternate exterior angles is ∠1 and ∠8. So the answer is A.

Step11: Solve question 10

Assuming the angle adjacent to ∠6 forms a linear - pair with a 40° angle. If the adjacent angle to ∠6 is 40°, then m∠6 = 140° (since they are a linear - pair). So the answer is D.

Answer:

1. A. Same - Side Interior Angles
2. D. Alternate Exterior Angles
3. C. Alternate Interior Angles
4. B. Corresponding Angles
5. B. m∠3 = 30°
6. C. m∠2 = 45°
7. D. ∠3 and ∠7
8. C. ∠5 and ∠3
9. A. ∠1 and ∠8
10. D. 140°