Question

If angle 1 and angle 2 are supplementary angles, and angle 3 and angle 2 are supplementary angles, what do you know about angle 1 and angle 3? Explain

Answer 1

Answer:

  angle 1 and angle 3 are congruent

Step-by-step explanation:

Angles supplementary to the same angle are congruent. Here both angles 1 and 3 are supplementary to angle 2, so angles 1 and 3 are congruent.

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If you like, you can get there algebraically:

  m∠1 + m∠2 = 180

  m∠3 + m∠2 = 180

Subtract the second equation from the first:

  (m∠1 + m∠2) - (m∠3 + m∠2) = (180) - (180)

  m∠1 -m∠3 = 0 . . . . simplify

  m∠1 = m∠3 . . . . . . add m∠3

When angle measures are the same, the angles are congruent.

  ∠1 ≅ ∠3