9514 1404 393
Answer:
- congruent
- x = 19
- ∠4 = 87°
Step-by-step explanation:
The marked angles are all "interior" -- between the parallel lines. Ones on the same side of the transversal (t) are called "same-side" or "consecutive" interior angles. Angles 1 and 4, 2 and 3 are pairs of consecutive interior angles.
Angles on opposite sides of the transversal are called "alternate" interior angles. Pairs 1 and 3, and 2 and 4 are pairs of alternate interior angles.
Alternate interior angles are congruent. Consecutive interior angles are supplementary (as are the angles of any linear pair).
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1) Angles ∠1 and ∠3 are congruent.
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2) Using the above fact, we can set the expressions for the angle measures equal to solve for x.
5x -2 = 2x +55
5x = 2x +57 . . . . . add 2
3x = 57 . . . . . . . . . subtract 2x
x = 19 . . . . . . . . . . divide by 3
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3) Angle 1 is ...
∠1 = 5x -2 = 5(19) -2 = 93
Angle 4 is its supplement.
∠4 = 180 -∠1 = 180 -93
∠4 = 87 . . . degrees
