Mathematics

Question

If line M is parallel to line N, which angle is supplementary with 1?

2 Answer

  • Prove: lines l and m are parallel. given ang 2 congruent to ang 5 1. ang 1 congruent to ang 2--colinear angle theorem 2 ang 5 congruent to
  • ∠2, ∠3, ∠6, ∠7 are supplementary angles to ∠1

    What are supplementary angels?

    Supplementary angles are those angles whose sum will be 180°.

    Fro the picture shown below,

    it is clear that the line M and N are parallel and cut by the transveral line L.

    So  ∠1 and ∠2 are supplementary angles because ∠1 and ∠2 are adjacent angles and are part of straight angle.

    Similarly, ∠1 and ∠3 are supplementary angles because ∠1 and ∠3 are adjacent angles and are part of straight angle.

    As line M is parallel to N

    and cut by by the transversal line L,  ∠1 and ∠7 are same side extrude angle.

    As we know the same side extrude angles are supplementary.

    so, ∠1 and ∠7 will be supplementary angles.

    As line L is cut by line N then, ∠6 and ∠7 are vertical angles.

    As we know the vertical angles are equal.

    ∠6=∠7

    From above it is clear that ∠1 and ∠7 will be supplementary angles.

    ∠1+∠7=180°

    ⇒∠1+∠6=180°  (as ∠6=∠7)

    so ∠1 and ∠6 will be supplementary angles.

    Therefore ∠2, ∠3, ∠6, ∠7 are supplementary angles to ∠1

    Learn more about the supplementary angles

    here: https://brainly.com/question/404323

    #SPJ2

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