Question

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

Given a∥b , and c is not parallel to a or b, which statements must be true?



Select each correct answer.

m∠7=m∠10

m∠4=m∠8

m∠8=m∠9

m∠2=m∠7
2.In this figure, AB¯¯¯¯¯∥CD¯¯¯¯¯ and m∠3=120°.

What is m∠6?
wo supporting reasons are missing from the proof. Complete the proof by dragging and dropping the appropriate reasons into each of the empty boxes.
Given: m∥nm∠1=120°

Prove: m∠6=60°

The figure shows what appear to be parallel lines n and m rising from left to right with line m above line n. Line p rises slightly from left to right first intersecting line n, then line m. The angles formed by the intersection of lines p and m are numbered from 1 through 4 in a clockwise direction starting with angle 1 which is located above line m and to the left of line p. The angles formed by the intersection of lines p and n are numbered 5 through 8 in a clockwise direction with angle 5 above line n and to the left of line p.

Statements Reasons
​ m∥nm∠1=120° ​ Given
∠5≅∠1
m∠5=m∠1 Angle Congruence Postulate
m∠5=120° Substitution Property of Equality
m∠6+m∠5=180°
m∠6+120°=180° Substitution Property of Equality
m∠6=60° ​ Subtraction Property of Equality

Answer 1

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°.

Answer 2

1. The correct options are 2 and 4.

2. The measure of angle 6 is 60°.

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°.