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≅∠T
, ∠N≅∠R
, ∠O≅∠S

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

∠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

Answer 1

To determine the congruent corresponding angles in triangles \( \triangle MNO \) and \( \triangle RTS \), we first list the angles in each triangle:

For triangle \( MNO \):

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

For triangle \( RTS \):

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

Now, we can pair the angles based on their measures:

• \( \angle M \) in triangle \( MNO \) measures \( 78^\circ \) and corresponds to \( \angle R \) in triangle \( RTS \) since they both measure \( 78^\circ \).
• \( \angle N \) in triangle \( MNO \) measures \( 34^\circ \) and corresponds to \( \angle T \) in triangle \( RTS \) since they both measure \( 34^\circ \).
• \( \angle O \) in triangle \( MNO \) measures \( 68^\circ \) and corresponds to \( \angle S \) in triangle \( RTS \) since they both measure \( 68^\circ \).

Thus, the pairs of congruent corresponding angles are:

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

This matches with the option: ∠M≅∠R, ∠N≅∠T, ∠O≅∠S.