Respuesta :
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.
[tex]\angle 2=\angle 6=\angle 3=\angle 7[/tex]
[tex]\angle 1=\angle 5=\angle 4=\angle 8[/tex]
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:
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°.