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In triangle MNO, m/M=78, m/N=34", and 2068" In ART'S, m/S = 68, m/R=78° and m/T 34 Describe the pairs of congruent corresponding angles in the two triangles. (1 point)

/M≈R, /N≈ /S,/O≈/T
/M≈R, /N≈ /T,/O≈/S
/M≈T, /N≈ /R,/O≈/S
/M≈S, /N≈ /T,/O≈/R

1 answer

To identify the pairs of congruent corresponding angles in triangles MNO and ART, we need to analyze the given angles:

In triangle MNO:

  • \( m/M = 78^\circ \)
  • \( m/N = 34^\circ \)
  • \( m/O = 2068^\circ \)

In triangle ART:

  • \( m/S = 68^\circ \)
  • \( m/R = 78^\circ \)
  • \( m/T = 34^\circ \)

Now, let's match the angles based on their measurements:

  1. From triangle MNO, we have \( m/M = 78^\circ \) which matches \( m/R = 78^\circ \) in triangle ART.
  2. Next, \( m/N = 34^\circ \) in triangle MNO matches with \( m/T = 34^\circ \) in triangle ART.
  3. The remaining angle in triangle MNO \( m/O \) is not stated correctly since it's beyond \( 180^\circ \); however, if we suppose it’s misrepresented and is meant to represent a proper angle, it would logically correspond to the remaining angle in triangle ART, which is \( m/S = 68^\circ \).

Combining these matches, we can see that the corresponding angles are:

  • \( m/M \approx m/R \)
  • \( m/N \approx m/T \)
  • \( m/O \approx m/S \) (assuming proper angle representation)

Thus, the correct choice would be: /M ≈ R, /N ≈ T, /O ≈ S.

So, the correct option is: /M ≈ R, /N ≈ T, /O ≈ S.