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

Mathematics

2 answers:

MAVERICK [17]4 years ago

8 0

Answer:

1. The correct options are 2 and 4.

2. The measure of angle 6 is 60°.

Step-by-step explanation:

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.

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°.

pantera1 [17]4 years ago

8 0

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