Question

unit 2 proficiency

1. what do we call the pairs of angles?

angles angle type (vertical, corresponding, alternate interior, same - side interior, or linear pair)
a. ∠1 and ∠2
b. ∠1 and ∠3
c. ∠2 and ∠3
d. ∠5 and ∠6
lines l and m are parallel. find ∠x and ∠abd and justify your answer (angle theorem).

Explanation:

Step1: Identify ∠1 and ∠2

Adjacent and supplementary, linear - pair.

Step2: Identify ∠1 and ∠3

On same side of transversal, corresponding.

Step3: Identify ∠2 and ∠3

Between parallel lines, alternate interior.

Step4: Identify ∠5 and ∠6

Adjacent and supplementary, linear - pair.

Step5: Find ∠x and ∠ABD for parallel lines L and M

∠ABD and 98° are same - side interior angles. Since lines are parallel, ∠ABD=180 - 98 = 82°. ∠x and 98° are corresponding angles, so ∠x = 98°.

Answer:

a. Linear pair
b. Corresponding
c. Alternate interior
d. Linear pair
∠x = 98°, ∠ABD = 82° (Same - side interior angles theorem for ∠ABD: sum of same - side interior angles of parallel lines is 180°; Corresponding angles theorem for ∠x: corresponding angles of parallel lines are equal)