Question

PLEASE HELP WITH QUIZ!!!!!!!! 25 POINTS!!!!!!!!!!!!!

Answer 1

Answer:

1. The correct options are 2 and 4.

2. The measure of angle 6 is 60°.

Step-by-step explanation:

1.

It is given that a∥b , and c is not parallel to a or b. So, we can not establish any relationship among the angles on the line a,b and  angles on the line c.

If a traversal line intersect two parallel line, then corresponding angles, alternate exterior angle and alternate interior angles are equal.

$\angle 2=\angle 6=\angle 3=\angle 7$

$\angle 1=\angle 5=\angle 4=\angle 8$

Therefore  correct options are 2 and 4.

2.

It is given that AB∥CD and m∠3=120°.

Statements                     Reasons

​ m∥nm∠1=120° ​                Given

∠5≅∠1                             Corresponding angles are equal

m∠5=m∠1                    Angle Congruence Postulate

m∠5=120°                    Substitution Property of Equality

m∠6+m∠5=180°             Supplementary angle property

m∠6+120°=180°            Substitution Property of Equality

m∠6=60° ​                    Subtraction Property of Equality

Therefore the measure of angle 6 is 60°.

Answer 2

Answer:

Step-by-step explanation:

It is given that a∥b , and c is not parallel to a or b. therefore, we can not create any relationship among the angles made on the line a,b and the angles on the line c.

If a traversal line intersect two parallel line, then corresponding angles, alternate exterior angle and alternate interior angles are equal, therefore using these properties, we have

m∠4=m∠8 (Corresponding angles) and m∠2=m∠7(Alternate exterior angle)

Therefore, correct options are 2 and 4.

2. Given: It is given that AB∥CD and m∠3=120°.

To prove: m∠6=60°

Proof:

Statements                               Reasons

1. ​ m∥n, m∠1=120° ​                        Given

2. m∠5≅m∠1                             Corresponding angles

3. m∠5=m∠1                      Angle Congruence Postulate

4. m∠5=120°                    Substitution Property of Equality

5. m∠6+m∠5=180°             Supplementary angle property

6. m∠6+120°=180°            Substitution Property of Equality

7. m∠6=60° ​                    Subtraction Property of Equality

Therefore the measure of angle 6 is 60°.