Question

I need help please!!!

Answer 1

9514 1404 393

Answer:

  (a) ∠3 and ∠5, or ∠4 and ∠6

  (b) ∠1 and ∠5, or ∠2 and ∠6, or ∠3 and ∠7, or ∠4 and ∠8

  (c) ∠1 and ∠7, or ∠2 and ∠8

Step-by-step explanation:

This is basically a vocabulary question. The words more less mean the following:

  alternate - on opposite sides of the transversal

  interior - between the parallel lines

  exterior - outside the parallel lines

  corresponding - in the same direction from the point of intersection

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We can say this about the angles of interest with respect to the angle numbering shown. (Angles are not always numbered this way.)

(a) Alternate interior angles - interior angles whose numbers add to give 8 or 10. ∠3 and ∠5, or ∠4 and ∠6

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(b) Corresponding angles - angles whose numbers differ by 4.

  ∠1 and ∠5, or ∠2 and ∠6, or ∠3 and ∠7, or ∠4 and ∠8

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(c) Alternate exterior angles - exterior angles whose numbers add to give 8 or 10. ∠1 and ∠7, or ∠2 and ∠8

_____

Additional comment

All of these pairs of angles are congruent pairs. You will see this means all acute angles are congruent, and all obtuse angles are congruent (when the lines are parallel). Of course, the obtuse and acute angles are supplementary. (There is additional nomenclature describing those supplementary pairs.)