Given that lines a and b are parallel, what angles formed on line a when cut by the transversal are congruent with ∠6?
a) ∠1 and ∠2
b) ∠1 and ∠4
c) ∠2 and ∠3
d) ∠2 and ∠4

Angle ∠6 will be the same magnitude =equal to angle ∠2 and angle ∠3

When parallel lines get crossed by a transversal some angles will be formed (which have the same magnitude = equal)) :

Corresponding Angles: The angles on the same corners

Alternate Interior Angles: Alternate sides of the Transversal, and on the Interior of the two crossed lines.

Alternate Exterior Angles: on the outer side of each of the two lines and on the opposite side of the transversal.

Then in the picture above:

Corresponding Angles: angles ∠1 & ∠5, ∠2 & ∠6, ∠3 & ∠7,∠4 & ∠8

Alternate Interior Angles: angles ∠4 & ∠5 and ∠3 & ∠6

Alternate Exterior Angles: angles ∠1 & ∠8, and ∠2 & ∠7

So that the angle ∠6 will be the same as the angle ∠2 (Corresponding Angles) and ∠3 (Alternate Interior Angles)

the steps for constructing a copy of an angle

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the angle x whose radians measure is given

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Keywords: Corresponding Angles, Alternate Interior Angles, Alternate Exterior Angles, a transversal

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: