With 25 !
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

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.

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°.

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°.

$12. that is my answer.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet