In △MNO

Question

, m∠M=78°
, m∠N=34°
, and m∠O=68°
. In △RTS
, m∠S=68°
, m∠R=78°
, and m∠T=34°
. Describe the pairs of congruent corresponding angles in the two triangles.(1 point)
Responses

∠M≅∠S
, ∠N≅∠T
, ∠O≅∠R

angle upper M congruent to angle upper S , angle upper N congruent to angle upper T , angle upper O congruent to angle upper R

∠M≅∠R
, ∠N≅∠S
, ∠O≅∠T

angle upper M congruent to angle upper R , angle upper N congruent to angle upper S , angle upper O congruent to angle upper T

∠M≅∠R
, ∠N≅∠T
, ∠O≅∠S

angle upper M congruent to angle upper R , angle upper N congruent to angle upper T , angle upper O congruent to angle upper S

∠M≅∠T
, ∠N≅∠R
, ∠O≅∠S

Answer 1

To determine the pairs of congruent corresponding angles in triangles \( \triangle MNO \) and \( \triangle RTS \), we can compare the angles of both triangles.

Given:

• In \( \triangle MNO \):

  • \( m\angle M = 78° \)
  • \( m\angle N = 34° \)
  • \( m\angle O = 68° \)

• In \( \triangle RTS \):

  • \( m\angle R = 78° \)
  • \( m\angle S = 68° \)
  • \( m\angle T = 34° \)

Now we can match the angles:

1. \( \angle M \) in \( \triangle MNO \) (78°) corresponds to \( \angle R \) in \( \triangle RTS \) (78°). Therefore, \( \angle M \cong \angle R \).
2. \( \angle N \) in \( \triangle MNO \) (34°) corresponds to \( \angle T \) in \( \triangle RTS \) (34°). Therefore, \( \angle N \cong \angle T \).
3. \( \angle O \) in \( \triangle MNO \) (68°) corresponds to \( \angle S \) in \( \triangle RTS \) (68°). Therefore, \( \angle O \cong \angle S \).

Thus, the pairs of congruent angles are:

• \( \angle M \cong \angle R \)
• \( \angle N \cong \angle T \)
• \( \angle O \cong \angle S \)

The correct option describing these pairs is: ∠M≅∠R, ∠N≅∠T, ∠O≅∠S.